J. Am. Chem. Soc. 1992, 114, 10338-10357
10338
this we include in Figure 4 three Ni atoms that are not in 1 but that would be present were the ideal hcp Ni crystal to continue16 We conclude that the interface between the NiSe portion of 1 and the Ni portion of 1 is exactly the six Ni atoms that are common to both. Note that the Ni-Ni bonds in the central Ni13unit of the cluster are on average longer than Ni-Ni bonds in elemental Ni. It is more common for the lattice parameters of nanoclusters of extended solids to be smaller than the corresponding values for those solids. This is usually explained by invoking the surface tension of the solid generating a 'Laplace pressure" which compresses the cluster to give shorter internal bond distances. The equivalent chemical explanation is that the otherwise unsatisfied valences on the surface of the cluster are satisfied by surface reconstructions which cause compression of the internal lattice. In the case of 1 the bonding sites external to the Ni,, core are satisfied by the NiSe cap (in addition to the three Sel atoms and three phosphine ligands which cap the bottom of the cluster), thus the compression of the Ni13core to a density higher than that of Ni is avoided. In other words, the lattice matching between the Ni core and the NiSe shell force a net expansion of the internal Ni lattice. The cluster 1 shows structural features of both NiSe and Ni, while the solid-state products of its thermolysis include Ni3Se2 and not NiSe. The path by which 1 disproportionates to give the ~~~~~~~~~~~
~
~
(16) The layered description of the Ni,9core of 1 is similar to that shown by Teo and co-workers for Au- and Ag-based clusters: Teo, B. K.; Zhang, H.; Shi, X. J . Am. Chem. Soc. 1990, 112, 8552.
observed solids presumably, although not necessarily, involves the interdiffusion of the two halves of 1. The details of the disproportionation are certainly quite complicated and merit further study. Of similar complexity is the route by which 1 is formed from Ni and Se. It is interesting to speculate whether 1 is formed by the fusion of the 'Ni-half" and the "NiSe-Half" or by the assembly of some other different sets of atoms or fragments. Conclusions We have shown that Ni(COD)2 reacts with SePEt, at elevated temperature to give a mixture of Ni2Se2 and Ni, that the two combine at lower temperature to give the cluster 1, and that 1 gives a similar mixture of Ni3Se2and Ni on heating. We have determined the structure of 1 and analyzed it in terms of associated extended solids, showing it to be a molecular example of an intergrowth of NiSe and Ni. We have characterized the interface between the two members of the intergrowth, showing that interface to be six N i atoms which are included in both the NiSe and Ni substructures. Supplementary Material Available: Positional parameters for 1 (Table S l ) , thermal parameters for 1 (Table S2), complete list of interatomic distances and angles for 1 (Table S3), crystallographic data for inclusion of C atoms (Table S5), positional parameters for 1 including located C atoms (Table S6), and thermal parameters for 1 including located C atoms (Table S7)
(1 1 pages); table of observed and calculated structure factors (Table S4) ( 5 5 pages). Ordering information is given on any current masthead page.
Calculation and Electronic Description of Quadratic Hyperpolarizabilities. Toward a Molecular Understanding of NLO Responses in Organotransition Metal Chromophores David R. Kanis, Mark A. Ratner,* and Tobin J. Marks* Contribution from the Department of Chemistry and Materials Research Center, Northwestern University, Evanston. Illinois 60208-31 13. Received May 18. I992 Abstract: This contribution explores the use of the computationally efficient, chemically-oriented INDO electronic structure model (ZINDO) in concert with perturbation theory to relate molecular quadratic hyperplarizabilities to molecular architecture and electronic structure in transition metal chromophores. The ZINDO-derived second-order nonlinear optical responses are found to be in excellent agreement with the experiment for a variety of ferrocenyl and (arene)chromium tricarbonyl derivatives. The assumptions needed to describe nonlinear optical response in simple molecular orbital terms are presented, and their reliability is analyzed in a quantitative fashion. All of the ferrocenyl chromophores examined are found to closely resemble traditional organic r-electron chromophores in that intense MLCT transitions dominate the second-order response. A detailed examination of the modest second-order nonlinearities of the chromium arenes identifies two shortcomings that may be characteristic of many organometallic architectures: the intrinsic hyperpolarizability may be far greater than the experimentally accessible vectorial component of 3, (that directed along the dipole moment direction), and the electronic distribution about the metal centers in many organometallic structures is peudwentrosymmetric. This explains the relatively low nonlinearities of a number of recently reported organometallic chromophores. The design utility of the present computational formalism is illustrated by the calculation of the second-order response of a hypothetical organometallic chromophore having a very acentric electron distribution and, correspondingly,a larger calculated second-order response than any measured to date for an organometallic chromophore.
Introduction Substances that exhibit highly nonlinear optical (NLO) responses are currently of great scientific and technological interest.' While inorganic solids such as LiNbO, and KH2P04have traditionally been the NLO materials of widest interest, recent results suggest that molecule-based macroscopic r-electron ensembles possess many superior NLO characteristics. Specifically, molecule-based NLO materials offer ultrafast response times, lower *Authors to whom correspondence should be addressed at the Department of Chemistry.
dielectric constants, better processability characteristics (e.g., amenability to thin-film fabrication), and enhanced nonresonant NLO responses relative to the traditional inorganic solidse2 Since ( 1 ) (a) Boyd, R. W. Nonlinear Optics; Academic Press: New York, 1992. (b) Prasad, N. P.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (c) Eaton, D. F. Science 1991, 253,281-287. (d) Marder, S. R.; Beratan, D. N.; Cheng, L.-T. Science 1991, 252, 103-106. (e) Heeger, A. J., Orenstein, J., Ulrich, D. R., Eds. Nonlinear Optical Properties of Polymers. Marer. Res. Soc. Symp. Prm. 1988, 109. (f) Zyss, J. J . Mol. Electron. 1985, I , 25-56. (g) Williams, D. J. Angew. Chem., Int. Ed. Engl. 1984, 23, 690-703. (h) Shen, Y. R. The Principles of Nonlinear Optics; Wiley: New York, 1984.
0002-7863/92/1514-lO338$03.00/0 0 1992 American Chemical Society
J . Am. Chem. SOC.,Vol. 114, No. 26, 1992 10339
Organorransition Metal Chromophores the macroscopic nonlinear optical susceptibility of these moleculebased materials is ultimately govemed by the nonlinear optical characteristics of the constituent molecular chromophores, the search for novel molecules displaying optimal nonlinear optical properties is currently an intense area of research in both academia and industry. Organometallic structures are intriguing candidates for study as NLO chromophores by virtue of their low-energy, yet sometimes intense, electronic tran~itions.~Such linear optical characteristics are suggestive signatures of molecules exhibiting significant nonlinear optical response.* In addition, coordinating a ligand containing highly polarizable *-electrons to a metallic center having weakly bound valence electrons (Le., which is highly polarizable) could, in principle, yield electronic structures that exhibit enhanced optical nonlinearities. The great structural and electronic diversity available in metal-organic environments could furthermore introduce into chromophore design strategies a host of new tunable parameters not available in simple n-organic structures. Finally, organometallic subunits, by virtue of the large number of available coordination sites about a metal center, could conceivably be incorporated into macroscopic matrices through a variety of novel attachment schemes. Several reports have appeared in the recent literature quoting appreciable macroscopic second-order nonlinear optical susceptibilities for powders of transition-metal organometallic chromophore~.~" Two molecules, trans- l-ferrocenyl-2-(N-methylpyridinium-4-y1)ethylene iodide6 (1) and cis- 1-ferrocenyl-2-(4nitrophenyl)ethylene5 (2), were reported to possess rather large powder nonlinearities (220 and 62 X urea, respectively) and have sparked subsequent research activity in this area. However, in striking contrast to conventional organic systems, neither a chemically oriented rationalization of nor a quantitative quantum (2) (a) Marder, S. R., Sohn, J. E., Stucky, G. D., Eds. Materials for Nonlinear Optics: Chemical Perspectives; ACS Symposium Series 455; American Chemical Society: Washington, DC, 1991. (b) Khanarian, G., Ed. Nonlinear Opt. Prop. Org. Mater. III; Proc. SPIE-Int. SOC.Opt. Eng. 1990, 1337. (c) Khanarian, G., Ed. Nonlinear Opt. Prop. Org. Mater. II; Proc. SPIE-Int. SOC.Opt. Eng. 1990, 1147. (d) Hann, R. A., Bloor, D., Eds. Organic Materials for Nodinear Optics; Royal Society of Chemistry Monograph 69; Burlington House: London, 1988. (e) Chemla, D. s.,Zyss, J., Eds. Nonlinear Optical Properties of Organic Molecules and Crystals; Academic Press: New York, 1987; Vols. 1 and 2. ( f ) Williams, D. J., Ed. Nonlinear Optical Properties of Organic Molecules and Polymeric Materials; ACS Symposium Series 233; American Chemical Society: Washington, DC, 1984. (3) See, for example: (a) Lever, A. B. P. Inorganic Electronic Spectroscopy, 2nd ed.; Elsevier: Amsterdam, 1984; Chapter 5. (b) Geoffroy, G. L.; Wrighton, M. S. Organometallic Photochemistry; Academic Press: New York, 1979; Chapter 1. (4) (a) Kimura, M.; Abel-Halim, H.; Robinson, D. W.; Cowan, D. 0.J . Organomet. Chem. 1991, 403, 365-372. (b) Pollagi, T. P.; Stoner, T. C.; Dallinger, R. F.; Gilbert, T. M.; Hopkins, M. D. J . Am. Chem. SOC.1991, 113, 703-704. (c) Coe, B. J.; Jones, C. J.; McCleverty, J. A.; Bloor, D.; Kolinsky, P. V.; Jones, R. J. J . Chem. SOC.,Chem. Commun. 1989, 1485-1487. (d) Tam, W.; Calabrese, J. C. Chem. Phys. Lett. 1988, 144, 79-82. (e) Bandy, J. A.; Bunting, H. E.; Garcia, M. H.; Green, M. L. H.; Marder, S. R.; Thompson, M. E.; Bloor, D.; Kolinsky, P. V.; Jones, R. J. In ref 2d, pp 225-231. (f) Eaton, D. F.; Anderson, A. G.; Tam, W.; Wang, Y . J . Am. Chem. SOC.1987, 109, 1886-1888. (g) Calabrese, J. C.; Tam, W. Chem. Phys. Lett. 1987, 133, 244-245. (h) Anderson, A. G.; Calabrese, J. C.; Tam, W.; Williams, I. D. Chem. Phys. Lett. 1987, 134, 392-396. (i) Frazier, C. C.; Harvey, M. A.; Cockerham, M. P.; Hand, H. M.; Chauchard, E. A.; Lee, C. H. J . Phys. Chem. 1986, 90, 5703-5706. Lamberth, C.; Murphy, D. M.; Mingos, D. M. P. Spec. Publ. - R. Soc. Chem. 1991,91 (Org. Mater. Non-Linear Opt. 2), 183-189. (k) Lesley, G.;Yuan, Z.; Stringer, G.; Jobe, 1. R.; Taylor, N. J.; Koch, L.; Scott, K.; Marder, T. B.; Williams, 1. D.; Kurtz, S. K. Spec. Publ. - R. SOC.Chem. 1991.91 (Org. Mater. Non-linear Opt. 2). 197-203. (1) Chiang, W.; Thompson, M. E.; Van Engen, D. Spec. Publ. - R. SOC.Chem. 1991, 91 (Org. Mater. Non-linear Opt. 2), 210-216. (m) Nalwa, H.S. Appl. Organomet. Chem. 1991, 5 , 349-377. (n) Zhang, N.; Jiang, M. H.; Yuan, D. R.; Xu, D.; Tao. X.T.; Shao, Z . S. J . Cryst. Growth 1990, 102, 581-584. (0)Tao, X.; Zhang, N.; Yuan, D.; Xu,D.; Yu, W.; Jiang, M. In ref 2d, pp 385-389. (p) Sakaguchi, H.; Nagamura, T.; Matsuo, T. Jpn. J . Appl. Phys. 1991, 30, L377-L379. (9) Richardson, T.; Roberts, G. G.; Polywka, M. E. C.; Davies, S. G.Thin Solid Films 1989, 179, 405-411. (5) Green, M. L. H.; Marder, S. R.; Thompson, M. E.; Bandy, J. A,; Bloor, D.; Kolinsky, P. V.; Jones, R. J. Nature 1987, 330, 360-362. (6) Marder, S. R.; Perry, J . W.; Schaefer, W. P.; Tiemann, B. G.; Groves, P. C.; Perry, K. In ref 2c, 108-115.
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chemical prescription for optimal responses in organometallic structures is currently available. Moreover, despite intense research efforts in this area, all microscopic second-order nonlinear responses (&-) reported for organometallic chromophores to date are considerably less than those of their r-electron organic counterparts.'J In this contribution, we report the first theoretical investigation of organometallic structures as second-order nonlinear optical chromophores using the accurate, chemically oriented, computationally efficient ZINDO-SOS quantum chemical formalism. By comparing computed quadratic hyperpolarkabfities with recent organometallic solution phase DC electric field-induced second harmonic generation (EFISH) data,7q8we are able to demonstrate the reliability of this approach, rationalize known molecular responses, suggest chemical modifications that should lead to greater nonresonant second-order susceptibilities, and put forth general prescriptions for optimizing the j3 tensor in metal-containing chromophoric structures. The representative classes of organometallic chromophores examined in this work will be the derivatized ferrocenyl molecules and the modified (arene)chromium tricarbonyl complexes. One can envision four generic classes of transition-metal organometallic architectures which could, in principle, yield enhanced second-order nonlinear optical responses. They are (1) structures possessing spectroscopicallyintense metal-teligand charge-transfer (MLCT) or (2) ligand-to-metal charge-transfer (LMCT) excitations, (3) organometallic or classic Werner type complexes where the metal atom(s) act(s) as an intermediary between an electron donor and an electron acceptor moiety, and (4) molecules which do not fit within the usual criteria for enhanced responses in nonlinear optical templates. In this contribution, we discuss the fundamental principles associated with exploiting MLCT bands in organometallic chromophores. This class of chromophores has been the most widely studied of the four and arguably offers the greatest promise for incorporation into x ( ~materials. ) Future contributions will address the electronic origin of the second-order response for classes 2-4. The underlying rationale for exploiting MLCT bands in frequency doubling is simple to understand. If an isolated ligand possessed a strong ?r to r * charge-transfer transition, linking a metal fragment to the ligand *-network might introduce an optical charge-transfer transition from a "nonbonding" metal-based state to the ligand-based **-state. As shown schematically in Figure 1, the energy of the MLCT band is expected to be at lower energy than that of the predominant ?r to T* transition in the isolated ligand. Researchers have long recognized the importance of having low-lying charge-transfer states for optimizing nonresonant nonlinear optical responses.; Therefore, it should, in principle, be possible to design metal-organic architectures possessing enhanced nonresonant second-order responses relative to those of uncoordinated organic moieties. Calculational Details A quantitative description of molecular nonlinear optical response is derived from a power series expansion of the molecular dipole moment (polarization) upon interaction with an oscillating external electromagnetic field (eq I ) . '
Here p i is the molecular polarization induced along the ith axis, El is the j t h component of the applied electric field, a is the linear polarizability, (7) Cheng, L.-T.; Tam, W.; Meredith, G. R.; Marder, S. R. Mol. Cryst. Lia. Crvst. 1990. 189. 137-153. '(8) Calabrese, J. C.; Cheng, L.-T.; Green, J. C.; Marder, S. R.; Tam, W. J . Am. Chem. SOC.1991, 113, 7221-7232.
10340 J. Am. Chem. SOC.,Vol. 114, No. 26, 1992
Kanis et al.
x*
In the SOS treatment employed in this study, the ground state is taken as the Hartree-Fock single determinant, and the electronic stat= created by the perturbing laser field are treated as an infinite sum over unperturbed particle-hole states, where the individual components of the quadratic hyperpolarizability are given by eq 2.18
X*
t
t
d orbitel
lone pair
Isolated Ligand
1
Metal-Ligand Complex
Figure 1. Schematic representation depicting the predicted effect on optical transitions of appending a metal fragment to an organic ligand.
8, the quadratic hyperpolarizability, and 7 , the cubic hyperpolarizability.
a,@, and y describe the responsivity of the molecule to an electromagnetic perturbation and are constants for a given molecular geometry. The 8 tensor is responsible for second-harmonic generation (SHG) and is the quantity of interest in this work. Several theoretical approaches for accurately calculating @ tensors have appeared in the literature. Computationally intensive methods such as coupled Hartree-F~ck,~derivative Hartree-Fock,’O and correlated wave’’ a b initio procedures are presently applicable to molecules of only limited size. The number of valence electrons in the chromophoric structures examined herein and the current lack of suitable extended transition-metal basis sets prohibit employing any of these rigorous treatments in the present study. Rather, the structurally elaborate chromophores of interest here will be treated within a perturbative framework where the electronic states mixed by the laser field are expressed as a sum over excited particle-hole states (SOS). Since the nonlinear optical expansion coefficients are functions of linear optical properties such as excitation energies and dipole matrix elements, the necessary electronic structure information can be conveniently obtained from a spectroscopically based semiempirical electronic structure description. Indeed, previous sum-over-states studies have employed either a modified all-valence CNDO/S12 (Complete Neglect of Differential Overlap), a r-electron PPP’) (Parr-Pariser-Pople), or, more recently, an all-valence INDO/S’&’6 (Intermediate Neglect of Differential Overlap) formalism to compute frequency-doubling efficiencies. These computationally efficient, chemically oriented quantum chemical methods have been remarkably successful at both predicting and rationalizing observed nonlinear optical responses for r-electron organic chromophores. Here we employ, for the first time, the transition-metal I N D O / S formalism (ZINDO)” to describe the second-order N L O response of transitionmetal-containing chromophores. ~~~
~~
(9) (a) Karna, S. P.; Prasad, P. N.; Dupuis, M. J . Chem. Phys. 1991,94, 1171-1181. (b) Meyers, F.; Adant, C.; Bredis, J. L. J . Am. Chem.Soc. 1991, 113, 3715-3719. (c) Caves, T. C.; Karplus, M. J. J. Chem. Phys. 1969, 50, 3649-3661. (IO) Dykstra, C. E.; Jasien, P. J. Chem. Phys. Lett. 1984, 109, 388-393. (1 1 ) (a) Sekino, H.; Bartlett, R. J . Chem. Phys. 1991,94,3665-3669. (b) Rice, J. E.; Amos, R. D.; Colwell, S. M.; Handy, N. C.; Sanz, J. J . Chem. Phys. 1990,93,8828-8839. (c) Sekino, H.; Bartlett, R. J . Chem. Phys. 1986, 85,976-989. (d) Subbaswamy, K. R.; Mahan, G. D. J . Chem. Phys. 1986, 84, 3317-3319. (12) (a) Morley, J. 0. J. Am. Chem. SOC.1988, 110, 7660-7663. (b) Docherty, V. J.; Pugh, D.; Morley, J. 0. J. Chem. SOC.,Faraday Trans. 2 1985, 81, 1179-1192. (c) Garito, A. F.; Teng, C. C.; Wong, K. Y.; Emmankahamiri, 0. Mol. Crysf.Liq. Crysf. 1984, 106, 219-258. (d) Lalama, S. L.; Garito, A. F. Phys. Rev. 1979, 20, 1179-1194. (e) Morrell, J. A.; Albrecht, A. C. Chem. Phys. Lett. 1979, 64, 46-50. (13) (a) Li, D.; Ratner, M. A.; Marks, T. J. J . Phys. Chem. 1992, 96, 4325-4336. (b) Soos, Z. G.; Ramasesha, S. J. Chem. Phys. 1989, 90, 1067-1076. (c) de Melo, C. P.; Silbey, R. J . Chem. Phys. 1988, 88, 2567-2566. (d)Li, D.; Marks, T. J.; Ratner, M. A. J. Am. Chem. Soc. 1988, 110, 1707-1715. (e) Li, D.; Marks, T. J.; Ratner, M. A. Chem. Phys. Lett. 1986, 131, 370-375. (f) Dirk, C. W.; Twieg, R. J.; Wagniere, G. J. Am. Chem. SOC.1986, 108, 5387-5395. (14) (a) Kanis, D. R.; Ratner, M. A.; Marks, T. J.; Zerner, M. C. Chem. Mater. 1991, 3, 19-22. (b) Kanis, D. R.; Ratner, M. A.; Marks, T. J. J . Am. Chem. Soc. 1990,112, 8203-8204. (c) Ulman, A.; Willand, C. S.; Kohler, W.; Robello, D. R.; Williams, D. J.; Handley, L. J . Am. Chem. SOC.1990, 112, 7083-7090. (d) Ulman, A. J . Phys. Chem. 1988, 92, 2385-2390. (e) Parkinson, W. A.; Zerner, M. C. J . Chem. Phys. 1989, 90, 5606-5611. ( 1 5) A coupled HartreeFock study incorporating an INDO Hamiltonian has been carried out on classical organic chromophores. Zyss, J. J . Chem. Phys. 1979, 70, 3333-3340. (16) Kanis, D. R.; Marks, T. J.; Ratner, M. A. In?. J . Quantum Chem. 1992, 43, 61-82. (17) Anderson, W. P.; Edwards, W. D.; Zerner, M. C. Inorg. Chem. 1986, 25. 2728-2732.
Here w is the frequency of the applied electric field, id,, = ( $dlil$n) is the matrix element of the displacement operator di)along the ith molecular axis between electronic states $, and $,,, w’,, = inn - igg is the dipole moment difference between the excited state and ground state (denoted by g), and hw, is the energy separation between the groundstate and an excited-state $,,. The transition moment matrix elements are computed in dipole length form using LCAO-MO coefficients and the Pariser appr~ximation’~ for matrix elements over atomic orbitals (eq 3). where R i , is a Cartesian coordinate. In this treatment, as in other
i, =, 6,,Ri,
(3)
semiempirical approaches that compute linear and nonlinear optical properties, the monoexcited configuration interaction (MECI) approximationZois employed to describe the excited states. In principle, all possible monoexcited states should be included in the summation over $,, and $d in eq 2; however, it will be seen that the computed second-order response converges without including all possible excited states of the valence basis. In the computations reported here, the 100 lowest energy transitions between S C F electronic configurations were chosen to undergo CI mixing and the resulting 100 states were then summed over in eq 2. The validity of truncating the infinite sum in eq 2 will be established later in this contribution. Although all 27 components of the B tensor can be computed, only the vector component along the dipole moment direction, j3, (eq 4), is sampled experimentally in electric-field-induced-second-harmonic-generation (EFISH) experiments.2’ (4) Here, p is the ground-state molecular dipole moment and
8, = P,i, + f / , X ( 8 , +
P,ij
+ Pjjt)
(5)
If!
where i and j run over the molecular Cartesian directions x , y , and z . Another quantity of interest in this work is the total quadratic hyperpolarizability, j310,(eq 6). 8, will be identical to &, when the charge
Pm, = q(P2 + P,2 +) :0
(6)
transfer is unidirectional and parallel to the molecular dipole moment. Note that &o, is always a positive quantity regardless of the sign of the individual vectorial components. It is conceivable that a molecule could have a large nonlinear optical response, but not along the molecular axis sampled by the EFISH measurement, so that &, would differ substantially from fi,,. This situation might be found in organometallic molecules having MLCT transitions, since the metal orbitals involved in charge transfer are usually significantly “nonbonding” in the ground state (18) Ward, J. F. Rev. Mod. Phys. 1971, 37, 1-18. (19) Pariser, R.; Parr,, R. G. J . Chem. Phys. 1953, 21, 466-471. (20) Linderberg, J.; o h m , Y. J. Chem. Phys. 1967, 49, 716-727. (21) Levine, B. F.; Bethea, C. G. Appl. Phys. Lett. 1974, 24, 445-447.
J. Am. Chem. SOC.,Vol. 114, No. 26, 1992 10341
Organotramition Metal Chromophores (Le., do not appreciably contribute to the ground-state dipole moment). We compare here our theoretical &, results to a recently tabulated, internally consistent set of EFISH data.’J In using EFISH results from a single laboratory, we minimize deviations due to experimental conditions such as differing incident frequencies, solvent polarities, local field models, and data reduction schemes. The EFISH, optical spectral, and dipole moment data quoted in this work were measured in relatively nonpolar solvents and with an incident laser frequency of 1.91 pm (ho = 0.65 eV). The ZINDO semiempirical formalism employed in this study has been discussed in detail elsewhere.17*22This computationally efficient scheme provides an accurate, chemically oriented description of linear optical properties for a wide range of transition-metal-containing structures. Molecular integrals are either computed rigorously, neglected, approximated with atomic parameters (ionization potentials, one-center coulomb integrals), or evaluated using a minimal number of well-defined empirical parameters (one parameter per atom). For the present N L O investigation, the ZINDO algorithm was implemented without any parameter manipulation or basis function alteration.’7*22All nonlinear optical computations were performed on a Stellar 2000 minisupercomputer, and all molecular NLO computations required less than 30 min of CPU time per molecule. The geometrical coordinates chosen for the present calculations were based on published crystallographic data. We have previously demonstrated that idealized nuclear coordinates are a legitimate alternative to optimized structures for input in N L O calculations, and all molecular structures in this work were idealized in accord with the prescription reported therein.I6 Bond distances and angles of organic fragments were those given previousIy,l6where the bridging polyene structures employed bond-alternating distances of 1.44-1.36-1.44 A. The ferrocenyl chromophore geometric parameters were based upon the crystal structure of ferrocene,23with Fe-C bond distances set at 2.04 A and cyclopentadienyl C - C distances at 1.40 A. The cyclopentadienyl stilbene portion of the trans ferrocenyl chromophore was chosen to be planar, while the stilbene fragment in the cis ferrocenyl stilbene analogues (2 and 5) was rotated out of the cyclopentadienyl plane by 30°, in accordance with the crystal structure of The nuclear coordinates for all Cr(CO),arene structures were based upon the crystal structure of the parent ($-benzene)chromium tricarbonyl chromophore (15).24 The geometry about the metal center was assumed to be octahedral with the Cr-C(arene) distances set at 2.20 A,the Cr-CO distance, at 1.84 A, the C - O distance, at 1.15 A, and all the arene C - C distances fixed at 1.40 A. The Cr-NH3 bond lengths employed in the hypothetical structures were taken to be 2.07 A, as found in a representative tetraamminechromium(II1) structure.2s
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Results and Discussion Sum over States Truncation. For the present ZINDO-SOS NLO computations, we have chosen to restrict the SOS summation and CI basis set to 100 excited configurations (vide supra). This has proven to be a valid approximation in computing , @, for archetypical donor-acceptor *-electron organic chromophores.I6 For example, in Figure 2a, the computed nonresonant second-order response for the prototypical organic chromophore, 4-amino-4’nitrostilbene, is plotted versus basis set size. The second-order , @ response reaches a converged value, which is in good agreement with the EFISH-determined response, with less than 50 excited states. Since the salient features of this plot are representative of those found for all *-organic chromophores examined to date,16 we now assume that a basis set size of 100 is sufficient for all second-order susceptibility calculations on conventional push-pull organic chromophores of similar molecular dimensions. In the case of transition-metal complexes, a significant number of “NLO inactive” ligand field (d-tod) transitions occur at a lower energy than the “NLO active” MLCT transitions. Therefore, one might anticipate that a relatively large CI basis set would be necessary to collect all of the @-determining charge-transfer (22) (a) Anderson, W.P.; Cundari, T. R.; Drago, R. S.;Zerner, M. C. Inorg. Chem. 1990, 29, 1-3. (b) Zerner, M. C.; Loew, G. H.; Kirchner, R. F.; Mueller-Westerhoff, U. T. J . Am. Chem. SOC.1980, 102, 589-599. (c) Bacon, A. D.; Zerner, M. C. Theor. Chim.Acta (Berlin) 1979, 53, 21-54, (d) Ridley, J.; Zerner, M. C. Theor. Chim. Acta (Berlin) 1973,32, 111-134. (23) (a) Takusagawa, F.; Koetzle, T. F. Acta Crystallogr., Sect. B 1979, 35, 1074-1081. (b) Dunitz, J. D.; Orgel, L. E.; Rich, A. Acta Crystallogr. 1956, 9. 373-375. (24) Bailey, M. F.; Dahl, L. F. Inorg. Chem. 1965, 4, 1314-1319. (25) Chang, J. C.; Gerdom, L. E.; Baenziger, N. C.; Goff, H. M. Inorg. Chem. 1983, 22, 1739-1744.
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StateBaais Set Sire
Figure 2. Plots of ZINDO-derived &, as a function of the number of state basis functions included in both configuration interaction and sumover-states expansion for (a, top) 4-amino-4’-nitrostilbene,(b, middle) trans-l-ferrocenyl-2-(4-nitrophenyl)ethylene,and (c, bottom) (4formy1pyridinyl)chromium pentacarbonyl.
transitions. As shown in Figures 2b,c, however, the calculated j3 response for two representative organometallic chromophores converges far below the 100 state size chosen for these studies. The approach to convergence of the organometallic curves is, however, slightly less steep than that for the stilbene derivative, suggesting that a slightly larger basis set is required for accurately describing,@ for organometallics than for organics. Nevertheless, the ZINDO-derived quadratic hyperpolarkabilities for these two representative organometallic chromophores converge well before the chosen basis set of size of 100. Since the calculated quadratic hyperpolarizability for the (pyridine)Cr(CO)5derivative is negative, the basis set convergence plot (Figure 2c) is a mirror image of those for the two positive@-chromophores(Figure 2a,b). The computed signs of the second-order responses are in agreement with e~periment;~ a qualitative rationale for these sign differences will be discussed in a subsequent c ~ n t r i b u t i o n . ~ ~
Kanis et al.
10342 J . Am. Chem. SOC.,Vol. 114, No. 26, 1992 n'
n
A
/
n
the third couples n with g through rsn. Fortunately, the complex mathematical description of the two-level contributions can be expressed in terms of the familiar quantities f (oscillator strength of a transition from g to n), hw, (energy tfference between g and n), and Algn (difference in dipole moments between n and g). If the summation in eq 7 is limited to one dominant transition and charge-transfer is unidirectional, as is usually the case for typical organic chromophores, the classic two-level model originally proposed by Oudar is obtained (eq BOudar
g
g
h~ g n f A l g n 3e2 =2 [(ho,)2 - (2hw)Z][(hw,)2
- (hw)Z]
(10)
27 individual tensorial elements into components along the ground-state dipole moment direction (&ec,2 and @vw,3) are given by eqs 4 and 5 . Ultimately, eq 9 is obtained. (9) = Bvcc.2 + Bvcc,3 Each two-level component in the infinite sum for &(kk.2 (eq 7) contains only two states, the ground state, g, and one exated state, n. As shown by the diagrammatic representation of the two-level process (Figure 3), the first photon couples n with the ground state through rgn,the second photon mixes n with itself via Arn, and
The three-level contributions in the SOS formalism (eq 8) contain a ground state and two excited states, n and n'. The first photon couples g with n through rp, the second photon mixes n and n'through r,, and the third connects n'with gvia rdg(Figure 3). Since detailed information on excited state-to-excited state (Le. two-photon) transitions (rad)is not currently available for most chemical systems, a qualitative, chemically-oriented description of these complex three-level mathematical expressions is not immediately evident. One might naively assume that the magnitude of &w,3 is significantly less than that of &,,z. Most chromophoric structures possess only one highly allowed electronic transition in the visible or near4 TV spectral region; that is, if r p is large, T~~ must necessarily be small. The product of r ,,rndrdg(generic three-level expression) should then be signiticantfy less than r Arjq (generic two-level expression) for most nonlinear ChromopForic structures. Howeverra ZINDO-SOS analysis reveals that many n'states can efficiently couple to a given n through large r, integrals. Thus, many large r , values for a given excited state n could potentially overcome the relatively small values of rdgto allow Bm3 to compete effectively with the one or two dominant terms in #3vw,2. Our computations suggest, therefore, that the three-level contributions cannot a priori be ignored when describing NLO responses with the ZINDO-SOS formalism.27 Returning to the basis set curves in Figure 2, we can now rationalize the characteristic shapes of these plots. In all three molecules, one excited state ( n ) is responsible for the observed maximum early in the summation. When additional states are included in the NLO calculations, the computed response shows a marked decrease in sharp disagreement with the simple twelevel model. We note that the general features of the basis set plots for these three chromophores are not unique to this ~ o r k . ' ~ , ~ ~ While such a decline has been noted previously, no explanation for this curious effect has been advanced. Our analysis reveals that the marked decrease in B is due to many three-level contributions rather than to additional two-level mechanisms. For most of the chromophores we have examined to date, all threelevel terms are of opposite sign from the dominant two-level contribution. As shown in Figure 2, a number of excited states are involved in decreasing the observed response to the converged value via a three-level process. Clearly, the three-level contributions are important in describing the origin of the second-order response in these chromophores. Since the three-level terms are non-neghgible in these 8, results and since there is no chemically oriented model available to rationalize the contributions, how then can we rationalize the pv, values in familiar chemical terms? The empirical answer lies in the relative magnitudes of the three-level versus two-level contributions. The sum of the three-level terms is found to scale approximately as the sum of the two-level terms in nearly all organic and organometallic molecules examined to date. Specifically, the three-level terms reduce &, by approximately half We propose, therefore, that a qualitative the value of &,,2.30 description of the nonlinear optical response can be gleaned from
(26) For the chromium-pyridine complex, the ZINDO @,,value is compared with an EFISH &cc7 for the analogous tungsten derivative. This replacement was necessary due to the present computational limitations of the ZINDO procedure. (27) We are preparing a manuscript that will discuss this aspect of the NLO computations in greater detail.
(28) (a) Oudar, J. L. J. Chem. Phys. 1977, 67,446-457. (b) Oudar, J. L.; Chemla, D. S.J. Chem. Phys. 1977, 66,2664-2668. (29) Pugh, D.; Morley, J. 0. In ref 2e. (30) Perturbation-theoretic analysis rationalizes this behavior. Kanis, D. R.; Marks, T. J.; Ratner, M. A. Manuscript in preparation.
Two-Level Terms Three-Level Terms Figure 3. Diagrammatic representations of the two-level and three-level contributions to the second-order susceptibility.
Relative Importance of Three-Level Terms versus Two-Level Terms in the SOS Treatment of Nonlinear Optical Response. It is somewhat surprising that the salient features of Figure 2b,c strongly resemble those observed for the 4-amino-4'-nitrostilbene in Figure 2a. In fact, of the many hundreds of NLO chromophores investigated to date in this laboratory with the ZINDO-SOS method (organic and organometallic), only a handful do not possess a basis set curve with a distinctive maximum followed by a steep decline to approximately half the maximum value a t convergence. To rationalize NLO responses in terms of chemically based electronic structure arguments, we must briefly comment on several general features of these plots.27 This discussion requires that we decompose the SOS prescription for computing /3 (eq 2) into two components, @v,,2 and &,,3. We can partition the sum-over-states expression (eq 2) into two contributions, a so-called two-level term (eq 7, B i j k . 2 ) and a three-level term (eq 8, Bijk.3). The algorithms for converting the
,
1 (Udg
- w)(wng - 2w)
+
1 (wffg
+ w)(wng + 2w)
a,,
J. Am. Chem. SOC..Vol. 114, No. 26, 1992 10343
Organotransition Metal Chromophores
Table I. Comparison of Experimental and ZINDO-Derived Molecular Hyperpolarizabilities along the Dipole Moment Direction (&), ZINDO-Derived Total Intrinsic Hyperpolarizability (btOt)at 1.91 fim ( h w = 0.65 eV) for a Series of Ferrocenyl Derivatives'
and the
X
X-A
R
X-A
1
H H
n
isomer
1
E
1 1 1 1 1 1 2 3 1 1
z E E z E E E,E E,E,E E E
&",
&scexP'
BtOtCalC
PX"lC
p,calc
wy=lc
perpi b
67.6 68.9 20.7 21.0 -1 .o -7.4 -0.3 4.0 3 H H 30.8 30.8 -8.8 -0.5 -0.3 4.5 4 -8.2 CH, H 34.7 34.7 -0.5 -0.7 4.4 H H 5.49 -0.6 -5.4 -0.2 3.9 5 5.92 H H 9.72 9.76 -5.8 6 -0.4 -0.2 4.6 H H 15.1 17.2 -4.4 7 -3.5 -0.2 3.9 -8.5 8 H H 47.4 47.5 -0.9 -0.2 4.5 9 H 66.6 66.8 -8.8 H -1.2 -0.2 CN 21 25.6 29.0 -6.0 10 H -4.0 -0.3 5.3 -6.2 CN 35 28.4 31.9 11 -4.1 -0.8 6.0 CH3 -5.9 -5.9 -0.4 4.9 12 C-2,4-(NO,), H H 1 E 23 40.0 44.8 "Also included is the calculated dipole moment in the x, y . and z directions as defined above. All N L O data are in units of cm5 esu-I; all dipole moment data are in units of debyes. Negative dipole moments indicate negative charge buildup in the positive coordinate direction. bDipole moment and N L O data for molecules 2-8 are from ref 8 and for 10-12 from reference 7. 2
N-CH,+ C-NO; C-NO2 C-NO2 C-CN C-CN CCHO C-NO2 C-NO2 C-NO2 C-NOZ
A' H H
13 31 40 4.0 10 12 66
50.07 0
2 40.0-
0
a
.:
'$
5
3, R = H, A = NO2 4, R = CH,. A = NO2 6,R=H,A=CN 7, R = H. A =CHO
0 0
30.0:
0
D
!
5
0 0
20.0:
P
0
d I
a
i'
Q &n=2 9,n=3
-
O
O
I
O
M
M
4
0
M
6
0
7
0
Experimental pvef(lO" cm6em.', fiio- 0.65 eV)
NO,
I
p'
O
~..,.,..,.,....,...,,..,.,....,....,
0.0
Figure 5. Plot of ferrocenyl chromophore &, values computed by the ZINDO-SOS procedure versus experimental data from refs 7 and 8. The one anomalous ferrocenyl point (j3vccexPt = 23 X cm5 esu-I; &,"Ic = 40 X cms esu-I) is thought to arise from nonplanarity in the stilbene portion of chromophore 12.
12
Figure 4. Ferrocenyl chromophores examined in this study along with molecular identification scheme.
analyzing the charge-transfer states contributing to two-level terms of the quadratic hyperpolarizability, even though the &cc,3 contributions are non-negligible. The insight gained through the predictive ability of the ZINDO model in concert with this empirical assumption provide the best evidence for its application. Ferrocenyl Derivatives. The electronically asymmetric ferrocenyl chromophores possess the largest microscopic and macroscopic second-order optical nonlinearities reported to date for organometallic architectures. Results from ZINDO-SOS N L O response computations on twelve ferrocenyl derivatives (1-12, Figure 4) are summarized in Table I.31 It can be seen that there (31) The second-order nonlinear optical responses in this contribution differ The varslightly from those reported in our preliminary comm~nication.'~~ iances are due to slight metrical im rovements in the idealized structures, as explained in a recent contribution.P6 The most notable geometrical mcdification is in the polyene bridge portion of extended T-architectures. Specifically, the alternating single-double-singlebond distances in the bridging region were set at 1.44-1.36-1.44A, rather than assuming all C C distances to be 1.40 A. This alteration has the effect of reducing the calculated &, value by 10-40%, depending upon the specific chromophore.
is rather good agreement between calculated and experimental7,*
p,, values. The correlation between theory and experiment is
illustrated graphically in Figure 5 . Note that the quadratic hyperpolarizability ranges from 0.10 to 500 X cms esu-' for the incident radiation used in these experiments (1.91 ~ m ) . ~ ~ , ~ ~ However, even with the 10-20% uncertainty usually associated with EFISH measurements,' the ZINDO-SOS derived tensors are in favorable agreement with experiment. Moreover, if we superimpose the previously discussed p,, correlation plot for 25 *-electron organic chromophoresI6 onto Figure 5, we see that the ferrocenyl chromophore results fall on the correlation line (Figure 6).
An important electronic structural conclusion from the ZINDO-derived NLO efficiency results is that the inherent quadratic hyperpolarizability is essentially equal to the computed NLO response along the ground-state dipole moment direction (p,,). An explanation for this observation can be gained by examining (32) (a) Cheng, L.-T.; Tam, W.; Stevenson, S. H.; Meredith, G.R.; Rikken, G.; Marder, S. R. J . Phys. Chem. 1991, 95, 10631-10643. (b) Cheng, L.-T.; Tam, W.; Marder, S . R.; Stiegman, A. E.; Rikken, G.; Spangler, C. W. J . Phys. Chem. 1991, 95, 10643-10652.
10344 J. Am. Chem. Soc., Vol. 114, No. 26, 1992
Kanis et al.
120.0,
Ii
3 -p.
100.0
80.0
0.oq 0
,
,
I
,
40
,
,
.
,
80
,
'
~
im
,
~
1M)
~
~
2m
,
Exprimentel p,,,(10'gocm5e~u~1,ti0=0.65 eV)
Figure 6. Plot of ZINDO-derived &, values for 25 r-electron organic chromophores versus experimenti6overlaid onto Figure 5. The solid line represents a least-squares fit to the data points. Note that the slope of the line is somewhat less than unity. We attribute this largely to stabilization of the excited state in the solvation medium in which the experiments were performed. Such stabilization will decrease the energy denominators of eqs 2 and 10, thus leading to the increase of Bobscompared to 8,,1,.
the Cartesian components (px, p,,, pz) of the computed dipole moment vector. Specifically, the magnitude of the dipole moment in the z direction (i.e., along the cyclopentadienyl-iron-cyclopentadienyl axis) is very small for most chromophores of this class (- -0.3 D) and only slightly larger for chromophores containing permethylated Cp rings. However, the vast majority of the ground-state dipole moment is located in the stilbene chargetransfer plane ( x and y directions). Thus, it is not surprising that j3,, &,(pj3) in these structures. Placing acceptor substituents perpendicular to the primary charge-transfer direction (10, 11, 12) causes ,3j to deviate slightly from ptot,yet even in these structures, over 90% of the intrinsic nonlinearity will be sampled by EFISH. The ZINDO-derived N L O data clearly show that an EFISH measurement will detect the bulk of the second-order nonlinear optical response for this class of ferrocenyl chromophores. The one anomalous molecule in the ZINDO-SOS ferrocenyl data is the 2,edinitro derivative (12). For this particular molecule, cms esu-I) is nearly twice the calculated response (40.0 X the experimental value (21 X cm5 esu-I). However, when these results are compared with the response for the 4-nitrosubstituted species (3), (30.8 X cm5 esu-I calculated versus 34 X cm5 esu-l found by EFISH), it seems likely that a geometrical distortion occurs in 12. A priori, an additional nitro group in an ortho position should increase g,,, since it aids in stabilizing the predominant charge-transfer excited state of this molecule, thereby lowering the transition energy. The theoretical calculations are in agreement with chemical intuition; however, the EFISH-determined response actually decreases when the second nitro group is added. The only reported crystal structure which relates to this issue is that of ?ran~-2,2',4,4',6,6'-hexanitrostilbene, where both of the trinitro-substituted aromatic rings are rotated 60° out of ethyleneic plane.33 We believe a 60' distortion is far too great for 12. In order to qualitatively assess the potential for a geometrical distortion in 12, an MNDO molecular mechanics s t ~ d y was ~ ~ undertaken. J~ In this study, the FeCloH9moiety was replaced by a p-methoxyphenyl (CH30C6H5) group. The results of this computation suggest that ethyleneic H-ortho NO2 repulsions force the phenyl ring to rotate out of the chromophore plane by 10-20°. Such a distortion should
-
(33) Gerard, P. F.; Hardy, A. Acta Crystallogr., Sect. C 1988, 44, 1283-1287. (34) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. SOC.1985, 107, 3902-3909. (35) The MNDO molecular mechanics study was performed on the CRAY-XMP supercomputer at the Pittsburgh Supercomputer Center. Default parameters were used when optimizing bonds, angles, and dihedral angles in 12.
.
inhibit the degree of *-conjugation in the chromophore, thereby lowering the computed second-order response. A ZINDO-SOS calcultion on 12 with the acceptor phenyl group rotated 20° out cm5 esu-l) of the molecular plane yields a j3, value (24.3 X in quantitative agreement with the EFISH measurement. In the absence of definitive solution-phase evidence for such a structural perturbation, we have chosen to report only the response for the idealized planar structure in Table I along with a caveat regarding possible structural distortions. It is readily apparent from the ZINDO-SOS results that traditional qualitative arguments for enhancing second-order nonlinear optical responses in organic molecules are completely applicable to the present ferrocenyl chromophores. For instance, the greater the electronic asymmetry between donor (ferrocenyl) , ~ I and acceptor (A) groups,% the larger the measured and calculated @ responses. As the strength of electronic donor is increased by permethylating the cyclopentadienyl ring, an increase in both computed and observed optical nonlinearity occurs. This is illustrated by comparing a ferrocenyl derivative (3, 30.8 X cm5esu-l) with the corresponding permethylated analogue (4, 34.7 X cm5 esu-I). Also, the susceptibilities of ferrocenyl derivatives are largest for molecules containing the strongest electronic acceptors, nitro (3) > aldehyde (7) = cyano (6).36 The structure possessing the strongest electronic acceptor in this study, the cationic methylpyridinium derivative (1-largest organometallic x ( ~to) date),s is calculated to possess the largest j3 response in the ferrocenyl class. However, the inherent charge on this species has prohibited a solution-phase EFISH determination of the microscopic response. While one must be very cautious about inferring microscopic susceptibilities from macroscopic measurements, it is interesting to note that the ratio of x ( ~values ) for the two noteworthy ferrocenyl structures (220 X urea (1):62 X urea is virtually identical to the ratio of computed molecular j3 values of 67.6 X cm5 esu-I (1):21.0 X cms esu-] (2). A qualitative analysis of the respective crystal structural data reveals that the packing in both acentric crystal structures is, in fact, very ~ i m i l a r . ~ , ~ Also in accord with traditional organic chromophore design guidelines, greater electron delocalization in the ferrocenyl structures leads to enhanced second-order N L O responses. For example, as the number of connecting ethyleneic units in the organic ligand is increased from 1 (3) to 2 (8) to 3 (9), the calculated response increases rather dramatically from 30.8 X cm5 esu-I to 47.4 X cms esu-I to 66.6 X cm5 esu-I. Chromophore 9 was included in this study for comparative purposes even though no experimental data currently exist for this molecule. Finally, the calculated response for the prototypical cis-stilbene structure (2,20.7 X lCMcm5esu-l) is somewhat lower than that for the analogous trans derivative (3, 30.8 X cms esu-I), in accord with conventional chromophore design ~ i s d o m . ~ , ~ It is interesting to note that the macroscopic response of the cis derivative is the second largest in this class, yet the microscopic response is one of the smallest. This dramatically illustrates the effect subtle geometrical differences in molecular structure can have on the crystal-packing architecture and, indirectly, on the NLO response of molecular crystals. Of course, this is not a central issue in self-assembled structures or poled polymeric systems. In summary, the ZINDO-derived quadratic hyperpolarizabilities confirm, in a quantitative fashion, that the ferrocenyl derivatives follow qualitative design rules that have evolved for ?r-electron organic chromophores. While it is obviously important to reproduce with reasonable accuracy the experimental &, responses for the ferrocenyl chromophores, it is equally important to understand, in detail, the electronic origins of the second-order susceptibilities. Let us first discuss the properties associated with the ferrocenyl fragment. This group is usually considered to be an electron-donating substituent when linked to organic fragments,37aand the formation (2))596
(36) (a) Swain, C. G.; Lupton, E. C. J . Am. Chem. SOC.1968, 90, 4328-4337. (b) Hansch, C.; Leo, A.; Taft, R. W. Chem. Rev. 1991, 91, 165-195.
J . Am. Chem. SOC..Vol. 114, No. 26, 1992 10345
Organofransition Metal Chromophores
Table 11. Comparison of Experimental and ZINDO-Derived Optical Absorption Maxima (Amax) and Associated Oscillator Strengths U, for Various Ferroccnyl Derivatives" X-A
R
first transition X-A 1 2
3 4 5 6
I 8 9 10 11 12
NCH3+ C-NOZ C-NO2 C-NO2 C-CN C-CN C-CHO C-NO2 C-NO2 C-NO2 C-NO2
C-2,4-(NO2)2
R
A'
n
isomer
H H H CH3 H H H H
H H H H H H H H H CN CN
1
E
1
Z
1 1 1
E E
1
E E E,E E,E,E E E E
H H
CH3 H
H
1 2 3
1 1
1
550 480 496 533 460 466 474 500
Z
526 560 536
second transition(s) xcalc PI'
PI'
xcxpt
521 363 38 1 468 386 392 392 5 10 458 473 460 455
xcxpt b
0.04 0.04 0.01
0.01
380 325 356 366 308 324 338 382
0.01 0.01 0.02 0.07
348 366 366
0.01 0.01 0.01 0.01
398 350 354 351 31 1 317 324 377 395 359 363 355 413
0.51 0.60 0.90 0.76 0.56 0.96 1.07 1.26 1.60 0.89 0.70 0.46 0.31
"All energy data are in units of nanometers. bSpectroscopicdata (in dioxane) for 2-8 are from ref 8, 10-12, from ref 7, and 9, from ref 40. of a cation (FeCp2+)is a ubiquitous part of ferrocene chemistry.37 Thus, at an initial qualitative level, the relatively large nonlinear optical responses of the ferrocene-derived chromophores are anticipated; they are reminiscent of traditional organic *-chromophoric units, in that a ferrocenyl donor is linked through a Aconjugated network to a nitro acceptor. The reversible oxidation of ferrocene has been shown to involve depletion of a metal-based HOM0.37J8 Therefore, it is reasonable to anticipate that the optical "donor" in the ferrocenyl chromophore is the relatively nonbonding pair of predominantly iron-localized oxidatively accessible HOMO electrons. Two recent investigations have discussed ferrocenyl N L O chromophores in a quantum chemical context. Marder, Cheng, et al. have attempted to extract linear and nonlinear optical information from an extended-Hiickel ground-state calculation on 3;'~~ such oneelectron models generally do not provide quantitative accuracy. In addition, a recent finite-field study by Waite and P a p a d o p o u l o ~examined ~~ the CY and y properties of ferrocenyl derivatives; calculations using this formalism do not provide frequency-dependent response information. Since the ZINDOSOS responses discussed in the present study are derived from a reasonable semiempirical model with a consistent treatment of both ground and excited states, our procedure allows connections to be made between microscopic responses and molecular architecture/electronic structure. That is, we can pinpoint those features that lead to large or small responses in a particular class of chromophoric structures within a molecular orbital context. Scheme I enumerates the physically reasonable assumptions necessary to understand the electronic origins of the NLO response for the prototypical molecules trans-l-ferrocenyl-2-(4-nitropheny1)ethylene (3), which will serve as a generic model for all ferrocenyl chromophores examined in this work. Note that for this molecule (-41.0 X cm5 esu-I) is of opposite sign and approximately half the magnitude of gvccs(71.8 X l C Mcmsesu-I), in accord with the common observations previously discussed. In making the assumption that an understanding of the /3 response can be gained by analyzing all two-level contributions, we have (37) See,for example: (a) Nesmeyanov, A. N.; Perevalova, E. G.; Gubin, S. P.; Grandberg, K. 1.; Kozlovsky, A. G. Tetrahedron Lett. 1966, 22, 2381-2387. (b) Perevalova, E. G.; Reshetova, M. D.; Grandberg, K. I. Methods of Organometallic Chemistry: Organoiron Compounds; Ferrocene; Nauka: MOSCOW, USSR, 1983. ( c ) Gmelin Handbook ojlnorganic Chemistry: Fe-Organoiron Compounds, 8th ed.; Springer-Verlag: Berlin, 1986; . Pt. -A8, Ferrocene. (38) See,for example: Gubin, S. P. Pure Appl. Chem. 1970,23,463-487. (39) Waite, J.; Papadopoulas, M. G. J . Phys. Chem. 1991,95,5426-5431.
Scheme 1. Analysis of fl for Molecule 3 Two-level Eontribution (p,,,2) Three-level contribution (PV,$) Total (hw = 0.65 eV)
b,
71.8
-41.0 30.8
in unita of 1 O 3 O emseou.'
Assumption I: Threedeuel terms scale as two-leuel terms. Therefore, understanding two-level t e r m will provide qwlitatiue understanding of p.
76% of the t o t a l two-level contribution comes from one two-level term involving a MLCT at 354 nm with an oscillator strength of 0.91.
Assumption 2: The two-level Contribution is dominated ty one excited state. Therefore, understanding this excited state will prouide qualitative understanding of p.
vExoid s-t.
= 0.50 az, ., 5.
+
0.7:
.,
0 4 ~
5.
where 2a and 4a are filled orbitals and 5a i s an unfilled orbital.
Assumptwn 3 The kdetermrnrng excited state transitwn LS dominated by two transi. twns between molecular orbtfal confiumtions as drctated by the ZINDO CI cwffirents A descnptwn of these transitions wdl lead to a chemrcal interpretation of
P
reduced the nonlinear optical problem to an extension of the linear optical problem. That is, if a satisfactory description of the predominant electronic transitions can be obtained, a chemically oriented, molecular description of the second-order response will immediately follow. It is encouraging to note that the ZINDO algorithm has been shown to reproduce reliably the experimental features of ferrocene MLCT transitions.22b In Table 11, we tabulate the experimental and calculated details of the optical absorption spectra of the ferrocenyl chromophores 1-12. The theoretical and experimental data7q8for these molecules show two optical transitions, with the exception of the 2,4-dinitro species (12), where the calculated spectrum contains three transitions while only two are found experimentally. Note that the ZINDO-derived lowest energy "transitions" for all structures possess very small oscillator strengths (0.01-0.04) relative to those of the higher energy transitions (0.46-1.60). When the computed optical properties are compared with those from experiment, it can be seen that the ZINDO method reliably predicts the intense shorter wavelength transitions. However, it less accurately predicts the characteristics of the weak longer wavelength optical absorptions. For example, the ZINDO-derived optical transitions
10346 J. Am. Chem. SOC.,Vol. 114, No. 26, 1992 of the pyridinium ferrocenyl derivative (1) are at 398 nm cf = 0.71) and 521 nm cf= 0.04), while the observed absorptions occur at 380 nm cf= 0.8) and at 550 nm cf= 0.2).4"-"2 The ZINDO treatment clearly underestimates the strength of the low-energy linear transitions, even though the computed nonlinear optical properties are in agreement with experiment. As we will show, the reason for this is that the higher energy features are MLCT in nature and are responsible for the nonlinear response of these derivatives, while the lower energy excitations are ligand-field transitions, which are essentially irrelevant to the NLO response. To gain insight into the linear optical properties of ferrocenyl derivatives, we first analyze the absorption spectrum of ferrocene. The dominant spectral feature is a broad band near 220 nm1.43 Several significantly weaker transitions lie at lower energies, the most commonly quoted being at 440 nm.43 Both theoretica122b,M and e ~ p e r i m e n t a lstudies ~ ~ * ~ have ~ shown that the 440-nm transition is a ligand-field "d-d" excitation. The exact assignment of the highly allowed 220-nm transition remains controversial; however, theory and experiment agree that it is either LMCT or MLCT in origin (probably MLCT).22bv43-46 Toma and co-workers have investigated the substituent dependence of the ferrocenyl ligand-field This band is found to be very sensitive to electron-withdrawing substituents in arylferrocene derivatives4' and very dependent upon the electron such as those examined acceptor in 1-aryl-2-ferrocenylethylene~~~ in this contribution. Moreover, the magnitude of the bathochromic shift in these structures correlates well with the Hammett u+ parameter of the electron acceptor The transition with the 440-nm parentage can significantly red-shift when acceptor strength or delocalization length is increased.46 For example, a 471-nm transition (e = 1310 M-I cm-' in isooctane) is observed in CpFeCSH4-N02,and a 520-nm optical absorption (e = 5200 M-I cm-' in isooctane) is found in the optical spectrum of CpFeCSH4-N=N-CSH4FeCp. These "d-d" transitions are highly allowed relative to typical ligand-field transitions and are energetically located in the vicinity of the A, measured for the ferrocenyl chromophores. Toma and co-workers have also found these so-called ligand-field transitions to have very large e values (>5,000 M-I cm-I) in some cases.48 From the above discussion, it is not difficult to extrapolate to the electronic situation in 1, where the observed 5 5 h m transition is likely a ligand-field transition with some admixed cyclopentadienyl character. It is not unrealistic to assume that the ligands with large u+ coefficients found in chromophores 1-12 could red-shift the 440-nm ligand-field ferrocene absorption far into the visible. In addition, Laporte-forbidden ligand-field transitions can "steal" intensity from highly allowed chargetransfer transitions via coupling through appropriate vibrational modes.49 The magnitude of the coupling matrix elements will be particularly large for structures possessing MLCT or LMCT excitations in the energetic proximity of the ligand-field transi(40) Marder, S. R.; Perry, J. W.; Schaefer, W. P.; Tiemann, B. G. Organometallics 1991, 10, 1896-1901. (41) The oscillator strengths were estimated from the published optical Since spectrum for 140 using the formula&, == 4.319 X 10-9(tmax)(Au)l,2.42 we do not have actual optical spectra for the other chromophores discussed in this work, it is impossible to convert between molar absorbtivity and oscillator strength due to the Au quantity. (42) Suzuki, H. Electronic Absorption Spectra and Geometry of Organic Molecules; Academic Press: New York, 1967; p 9. (43) (a) Scott, D. R.; Becker, R. S.J . Chem. Phys. 1962,35,516-531. (b) Armstrong, A. T.; Smith, F.; Elder, E.; McGlynn, S . P. J . Chem. Phys. 1967, 4 6 , 4321-4328. (c) Sohn, Y. S.; Hendrickson, D. C.; Gray, H. B. J . Am. Chem. Soc. 1971, 93, 3603-3612. (44) (a) Rohmer, M. M.; Veillard, A,; Wood, M. H . Chem. Phys. Lerf. 1974,29,466-468. (b) Rosch, N . ; Johnson, K. H. Chem. Phys. Left. 1974, 2 4 , 179-183. (45) Tarr, 4. M.; Wiles, D. M. Can. J . Chem. 1968, 4 6 , 2725-2731. (b) Cerny. V.; Pavlik, I.; Kustkovi-Maxovi, E. Collect. Czech. Chem. Commun. 1976, 4 1 , 3232-3244. (46) Bozak, ,R. E. Adu. Phorochem. 1972, 8, 227-244. (47) Toma, S.; Giplovskf, A.; HudeEek, M.; Langfelderovi, Z. Monarsh. Chem. 1985, I L6, 357-364. (48) Toma, S.;Giplovskg, A.; ElePko, P. Chem. Pap. 1985, 39, 115-124. (49) (a) Reference 3a, Chapters 4 and 6. (b) Reference 3b, Chapter I .
(a)
Kanis et al. Table 111. Comparison of ZINDO-Derived &, Values for Ferrocenyl Derivatives and their Methoxyphenyl Analogues'
8"ec A' n H 1 H 1 H 2 H 3 CN 1 H 1 "All NLO
X= X = isomer FeCp(C,H,) CH30C6H4 Z 20.7 (2) 19.8 E 30.8 (3) 34.2 E,E 47.4 (8) 50.5 E,E,E 66.6 (9) 68.0 E 25.6 (10) 26.8 (2,4-dinitro species) 40.0 (12) 42.1 data are at hw = 0.65 eV in units of lo-'" cms esu-I.
ti on^.^^ The charge-transfer excitations in transition-metal molecules possessing significant metal-ligand covalency tend to display optical characteristics arising from the large effective coupling matrix elements.49 Thus, the highly covalent nature of the metal-ligand bonding is expected to increase the (formally forbidden) oscillator strengths of d-d transitions in the ferrocenyl structures far beyond what is observed in classical coordination complexes.49 Note that the Herzberg-Teller expansion of the full Hamiltonian that accomplishes the vibrational coupling is omitted in the present work. Therefore, it is not surprising that the present computational procedure does not reproduce the characteristics of the predominantly d-d transitions. There is thus compelling experimental and theoretical evidence that the low-energy transitions in 1-12 can be assigned as ligand-field-based. As such, they should contribute little to the NLO response. In addition to having modest fvalues, the small solvatochromic shift measured for these optical excitations relative to those for the allowed MLCT bands is indicative of a small Aggn.40 Our computations indicate that the weak ligand-field transition in the ferrocenyl prototype (3) can be described by a charge-transfer of 0.78 t2,-like electrons into 0.64 e,-like electrons and 0.14 cyclopentadienyl electrons. In essence, this represents a complete charge transfer from a metal-localized state of pseudo-t2, symmetry into a metal-localized state of pseudo-e, symmetry, resulting in a very small Ah. Therefore, while the d-d transition energies may be attractive for chromophore design, the small Ah and modest fvalues associated with these transitions argue against exploiting them in N L O chromophoric materials. In a simple two-level picture (eq IO), they are predicted to afford small values of p. We now turn to the shorter wavelength transitions in the ferrocenyl chromophores. If an MLCT assignment is correct, such excitations should dominate the second-order nonlinear optical response in chromophores 1-12. The h of this particular excitation can be traced back to the 243-nm transition in the parent ferrocene as shown by B ~ z a k Note . ~ ~ that most of the ZINDO-derived h values for the higher energy transitions are within 15 nm of the observed absorption energy, as shown in Table 11. The prototypical chromophore 3 illustrates the good agreement between theary and experiment for this transition (experiment = 356 nm, theory = 354 r ~ m ) . ~ lThe excellent agreement between theory and experiment for both the higher energy linear optical transition and the second-order quadratic hyperpolarizability strongly suggests that the lower energy ligand field-based optical transitions are essentially NLO inactive and that the intense MLCT bands dictate the N L O response in these structures. Interestingly, recent degenerate four-wave mixing experimentsS2suggest that only the higher energy transitions contribute significantly to the observed (50) Fenske, R. F. J . Am. Chem. Soc. 1967, 89, 252-256. (51) As one would anticipate from the distortion arguments presented earlier in this contribution, the computed absorption characteristics of the 2,4-dinitro derivative (12) are not in agreement with experiment and are an exception to the excellent correlation between theory and experiment. (52) Ghosal. S.; Samoc, M.; Prasad, P. N.; Tufariello, J. J. J . Phys. Chem. 1990, 94, 2847-2851.
J . Am. Chem. S O ~ .Vol. , 114, No. 26, 1992 10347
Organotransition Metal Chromophores
--- - - 4.03
4 . 4 8 4.08
-4.07
4.36
+O.W
-0.13 -0.55
Scheme 11. Analysis of @ for Molecule 13 Two-level contribution @,.,,Z~ Three-level contribution (pVec,3) Total (h w = 0.65 eV) eru.l p,, in unitd of 10.39
84.4
-50.2 34.2
Assumption 1: Three.leve1 terms scale as two.leue1 terms. Therefore, understanding two-level t e m will provide qualitative understanding of P. 4.18 -0.07 -0.54 -e86% of the total two-level contribution come8 from one two-level term involving a transition at 353 nm with an oscillator strength of 1.17.
Figure 7. The difference in electronic populations between ground state and crucial excited state for a prototypical ferrocenyl derivative and a traditional organic chromophore as determined by ZINDO calculations. A negative population is indicative of an increase in electron density in the charge-transfer process.
third-order responses in representative ferrocenyl chromophores. Specifically, the low-lying resonances (labeled as d-d) do not appear to make an important contribution to the third-order response in these molecules, while the higher lying resonances (labeled as T-x*) appear to dominate the third-order susceptibilityaS2 If in fact, one excited state is primarily responsible for the observed second-order susceptibility, the ferrocene derivatives should bear strong resemblances to classic two-level systems, such as the push-pull polyenes. As pointed out by Marder and Cheng? the experimental NLO response of 3 is essentially identical to that of the corresponding methoxyphenyl analogue 13.
13
In order to examine the relationship between classic organic chromophores and the ferrocenyl chromophores in more detail, we replaced the ferrocenyl group in selected chromophores with a methoxyphenyl (CH30-C6HS)moiety. From the results of this numerical study (Table 111),it is immediately obvious that this structural variation leaves the computed second-order response essentially unchanged. For example, the Is,, ratio of the organic to ferrocenyl analogue is 19.8120.7 for 2, 50.5147.4 for 8,and 42.7/40.0 for the anomalous dinitro derivative 12. This similarity strongly suggests that there is common electronic origin of the nonlinear optical response in these two classes of chromophores and that the predominantly metal-centered d-d excitations are unimportant in determining the NLO response. To further probe the connection between the ferrocenyl structures and their organic counterparts, the one charge-transfer state that dominates the N L O response in 3 and 13 will be analyzed. The calculated changes in charge between ground and excited state are shown in Figure 7. In each chromophore, the nitro acceptor group receives -0.55 electrons in the chargetransfer process. The ferrocene donor supplies 0.59 electrons to the a-network in the charge-transfer excitation in 3,with most of this charge density originating at the iron center. In 13,the methoxyphenyl moiety contributes 0.43 electrons to the charge transfer, with mast of the electron density derived from the phenyl group appended to the methoxy substituent rather than from the methoxy moiety itself. We have found this to be true for all push-pull stilbenes examined to date. That is, the phenyl group adjacent to the electron-donating moiety, rather than the donor group itself serves as the effective donor in the charge-transfer transition. In contrast, the NOz electron acceptor serves as the predominant electron sink in the charge-transfer transition. Overall, the change in regional electron populations associated with the dominant charge-transfer optical transition in 3 are virtually identical to those computed for 13,providing additional evidence for the strong N L O similarity between the ferrocenyl chromophores and their methoxyphenyl counterparts. The ZINDO-SOS algorithm permits decomposition of the state-to-state transitions dictating the NLO response into transitions between molecular configurations (i.e., transitions between
Assumption 2: The two.leve1 contribution is dominated by one excited state. Therefore, understanding this excited state will provide qualitative understanding of p.
P E x ~ l t d State
0.91'4,
.> 5s
where 4a is a filled orbital and 5a is an unfilled orbital.
Assumptwn 3 The ',%determining excited state transUron LS domrnated by one transitwn between molecular orbital confuuratwns os drctated by the ZINDO CI coeffrclents A descriptwn of fhrs transition will lead to a chemccal interpretation of
P
filled and unfilled molecular orbitals). For 13,the predominant excited state involves little CI mixing between configurations and is found to be primarily a HOMO to LUMO transition (Scheme 11). The data in Scheme I suggest that the important state in 3 involves significant CI mixing between two configuration transitions, one of them also a HOMO-LUMO excitation. By decomposing the computed response into configurational excitations and describing these excitations in molecular orbital terms, a chemically-oriented rationalization of the NLO response will emerge. Simplified molecular orbital diagrams depicting frontier orbital interactions in 3 and 13 are displayed in Figures 8 and 9, respectively. Note that all u interactions have been deleted from these pictures, since they have little effect on the nonlinear optical all responses. Since the molecular point group of 3 and 13 is CI, molecular orbitals are of &a"symmetry and can mix in both the SCF and CI portions of the computation. We have chosen to divide the two chromophores into a common pnitrovinylbenzene fragment combining with a ferrocenyl fragment in 3 and a methoxyphenyl fragment in 13. The common nitro-containing fragment possesses a HOMO that is primarily of ethyleneic bonding character and a LUMO of appreciably higher energy that is nitro-centered. The electronic details of the ferrocenyl fragment in 3 are straightforwardly related to the well-studied electronic structure of ferrocene.s3 The three lower lying metal orbitals in ferrocene (dxy dA9, and ds) are essentially the pseudo-"t * set of d, orbitals and are fully occupied in a d6 Fe(I1) system? While there is disagreements4over the exact ordering of these three orbitals in the parent ferrocene molecule, their relative positions are not crucial for our discussion. Also note the presence of two unoccupied metal orbitals a t significantly higher energy. These are the metal-ligand antibonding e, set commonly associated with octahedral structures. When the ferrocenyl fragment interacts with the styrenyl moiety, only one of the filled d, orbitals will be significantly perturbed by the interaction; the other two d, orbitals are virtually unaffected due to limited overlap (spatial constraints) with the wfragment. In-phase and out-of-phase linear combinations of the two interacting fragment orbitals produce molecular orbitals 2a and 4a (Figure lo), with the latter being the molecular (53) (a) The actual symmetry notation that we use for orbitals varies. For clarity, the crystal field notations e8 a n d tlg are useful for discussing metal d-levels. In actual MO calculations, it IS more appropriate and meaningful to use the proper point group symmetry ( 0 , . e , ) labels. (b) Lauher, J . W.; Hoffmann, R. J . Am. Chem. Soc. 1976, 98, 1729-1742 and references therein. (54) Cowley, A. H. Prog. Inorg. Chem. 1979, 26, 46-160.
10348 J . Am. Chem. SOC.,Vol. 114, No. 26, 1992
Kanis et al.
0
-1
-2 c 4
c
/
-7
,4a’Y‘,,
eV
,’ I ’
-
-8
I
2a
---------
-9
dZ2
la
-10
Figure 8. Molecular orbital diagram for the representative ferrocenyl chromophore 3.
HOMO. As detailed in Scheme I, it is precisely these two molecular orbitals that are involved in the “NLO-active” state-testate charge-transfer transition in 3. Specifically, 50% of the dominant optical excitation in 3 is 4a-to-LUMO in character, 25% is 2ato-LUMO, and the remainder is derived from a host of other configuration space excitations. From Figure 8 it is clear that orbitals 2a and 4a contain significant contributions from both interacting fragments. This covalent mixing reflects the energetic similarity of the respective orbitals. The result of configuration interaction for these two configuration space transitions is to constructively add the ferrocenyl (principally dxz+) contributions and destructively add the nitro-containing ligand (principally ethyleneic) components. In summary, the “donor” state is primarily iron in character with a small fraction of the electron density in the ethyleneic region. Over 95% of the iron contribution originates from the dxz-,,z orbital. The residual metal character (dxz).serves to point the d+.z function toward the r-electron density in the bridging region of the organic fragment, thereby increasing the overlap between the metal and organic fragments. The LUMO of the nitro fragment becomes the LUMO (orbital Sa) of 3 as depicted in the interaction diagram (Figure 8). The fragment orbital is essentially unperturbed (both spatially and energetically) upon interaction with the ferrocenyl fragment, since the majority of its electron density is spatially distant from the interaction region. This orbital is primarily centered on the acceptor group, so that modifying the accepting moiety should substantially alter the energy of this fragment orbital and subsequently the molecular LUMO as well. That is, a weaker acceptor moiety, such as a C N or COOCH3, will increase the SCF energy of the LUMO. Before using the orbital picture to rationalize trends observed for the j3, values in 1-12, we first analyze the 4-methoxy-4’nitrostilbene chromophore (13) within the molecular orbital formalism. The orbitals of the methoxyphenyl fragment (Figure 9) are derived from a bonding and antibonding interaction between
the phenyl ring and the methoxy lone pair. The bonding, lower energy fragment orbital is predominantly methoxy lone pair in character as pictured in Figure 9. This orbital is essentially unperturbed upon interaction with the nitro-containing moiety and results in the 3a molecular orbital. Somewhat surprisingly, the oxygen-based molecular orbital is not a major contributor in the charge-transfer excitation that dictates j3v,. The second methoxyphenyl orbital, the higher energy of the two fragment functions, is delocalized over the entire phenyl ring and therefore can efficiently interact with the ethyleneic-centered HOMO of the nitrecontaining fragment. The interaction between these two orbitals produces a stabilized M O (orbital 2a) and a highly destablized orbital (4a, HOMO). As was the case for 3, the LUMO of the pnitrostyryl fragment is essentially unperturbed by the interaction and becomes the LUMO (orbital 5a) of 13. As shown in Scheme 11, the excitation that dominates the second-order nonlinear optical response in 13 is accurately described by a 4a to Sa (HOMO to LUMO) transition. From the pictures of the relevant fragment orbitals in Figure 9, it is clear that the charge transfer will occur from the phenyl ring adjacent to the methoxy group to the nitro moiety. Recall this charge redistribution is exactly what the electron density change results suggested (Figure 7). Again, the orbital picture accurately represents the state-testate charge-transfer populations. At first glance it may seem surprising that the donor substituent in 13 does not play a more active role in the important charge-transfer transition associated with the large second-order NLO response. However, the donor moiety will indirectly influence the charge transition by raising the SCF orbital energies of the appended phenyl ring. The similarity of the M O orderings of the prototypical ferrocenyl chromophore and its methoxyphenyl analogue, as shown by Figures 8 and 9, is remarkable. The functional characteristics as well as the energetic values for the key molecular orbitals are virtually identical in 3 and 13. For example, both donor orbitals (d,z-,,2 in 3 and phenyl ring in 13) are nearly of equal energy and
J. Am. Chem. SOC.,Vol. 114, No. 26, 1992 10349
Organotransition Metal Chromophores
---_
5a
C
H
,
O
a
- na " '
\
NO,
.
W
N
O
z
Figure 9. Molecular orbital diagram for the corresponding methoxyphenyl analogue of 3.
covalently interact with ethyleneic bridge orbitals of the acceptor. In addition, the acceptor-based LUMOs in the two chromophores are essentially interchangeable. The admixture of 2a Sa in the dominant excitation (4a Sa) observed in 3 is somewhat larger than that found in 13 as expected from perturbation theory (the 2a I transition energy is closer to the 4a Sa excitation energy in 3 than it is to that in 13) as shown in Schemes I and 11. The dominant components of the important charge-transfer transition are similar in 3 and 13, but as Figure 7 shows, the real charge transfer originates mostly from the metal in 3 but from the 7r-donor in 13. To describe this properly, the simple HOMO LUMO transition appropriate for 13 is admixed (Scheme I) with 2a I in 3. Since similar charge-transfer patterns dominate the N L O response and chromophores 3 and 13 and their constituent electronic structures are very similar, it is perhaps not surprising that ferrocenyl and methoxyphenyl donor units produce similar NLO responses when introduced into conventional pushpull chromophoric architectures. One may wonder how traditional chromophore design guidelines are manifested in the M O diagrams of Figure 8 and 9, or more specifically, how experimentalists can use the orbital picture to rationalize NLO responses. As mathematically described in eq Ap f g n , and wgn (= E , / h , = 27rc/X,) are the crucial two-leveriarameters In chromophore design. For the present discussion, the oscillator strength U, in the Oudar formula will be rewritten as a function of rgn2and E , to yield the simplified, zero-frequency two-level prescription (eq 11). The energy of the
-
-
-
-
-
+
dominant excitation ( E or hc/X ) can be monitored by probing the perturbations of t8k orbitaffknergy levels involved in the charge-transfer transition. For example, permethylation of the cyclopentadienyl ring in the prototype raises the energy of the d,
donor orbital from 6.99 eV in 3 to 7.13 eV in 4. Since the derivatization should have little effect on the orbital energies of the acceptor levels (verified by our computations), the increase in d orbital energy should produce a bathochromic shift in the MLCT transition if effects due to CI remain approximately constant. As predicted, the principal optical transition in 3 (354 nm) shifts to 357 nm in the permethylated derivative 4. In a similar fashion, altering the acceptor moiety should significantly change the energy of the acceptor unit without affecting the donor. Therefore, decreasing the acceptor strength by replacing the nitro group with a C N (6) or COH (7) group should raise the SCF energy of the LUMO, thereby hypsochromically shifting the charge-transfer transition. As reported in Table 11, the experimentally measured MLCT excitation blue-shifts from 354 nm in 3 to 317 nm in 6 and 324 nm in 7. Similarly, increasing the acceptor strength should red-shift the dominant transition as is observed for 1. Limited qualitative information on the Ap quantity can also be obtained from the orbital picture. Quantum chemical computations in concert with M O arguments can determine if a particular charge-transfer excitation is effectively one-dimensional or multidimensional. The orbital pictures for 3, for example, indicate that the electronic redistribution associated with the dominant MLCT transition involves only one of the cyclopentadienyl rings. That is, two-dimensional or three-dimensional charge transfer, a situation that will greatly diminish Ah, is not an issue here. Unfortunately, there is no simple relationship between Ap and fragment energetics, as pointed out in a recent contribution.Id Thus, a more complete description of Ap within our model will require an atom-by-atom charge analysis such as that provided in Figure 7. Perhaps the most unique aspect of the ferrocenyl chromophores, in comparison with other organometallic nonlinear optiphores, is that they possess low-lying charge-transfer excitations with reasonably large oscillator strengths (>0.50). A rationale for these
10350 J . Am. Chem. SOC.,Vol. 114, No. 26, 1992
5a
4a
e 2a Figure 10. Frontier molecular orbitals of 3 involved in the dominant charge-transfer excitation. The excitation is comprised of a mixture of 2a -Sa with 4a Sa, to yield the population changes in Figure 7 . Note that adding 2a to 4a gives destructive interferenceeverywhere except on the metal center; this, then, is the source for charge-transfer.
-
anomalously large oscillator strengths ( a r 2, is available through the orbital pictures of Figures 8 and 9. Kamining the physical interpretation of rgn(transition moment) between a ground state (represented by a donor molecular orbital) and an excited state (represented by an acceptor molecular orbital) for a traditional *-electron organic chromophore affords a qualitative understanding of the “allowedness” of a given transition. The transition moment ( r p ) for the dominant T ** excitation in a *-organic chromophore can be written as e(J.JxlJ.,,), assuming x is the charge-transfer direction. For push-pull species, such as those of interest here, the dominant transition is from the HOMO (largely centered in the donor region, with some extension onto the ethyleneic bridge) to the LUMO (largely acceptor-centered, with some ethyleneic bridge extension). The overlap density, and therefore the integral, will vanish unless both HOMO and LUMO have significant extension onto the ethyleneic bridge.5s From these rather simplified arguments, it appears that reasonable oscillator strengths in highly asymmetric (large Ab) chromophores will only occur in significantly covalent structures. That is, a non-negligible amount of electron density must be present in the *-backbone bridge of potential chromophores. In the specific case of stilbene-based derivatives, the crucial functions are the pI functions on the ethyleneic carbon atoms. Our prototypical chromophores 3 and 13 meet the large fgn criterion, as can be Seen in Figures 8,9, and 10. The chargetransfer transitions in both structures possess non-negligible electron densities in the intermediate region. If the nitro group is replaced by a weaker acceptor, relatively more electron density should be present in the bridging region, and this may be associated with an increase in the relevant oscillator strength. As reported in Table 11, the oscillator strength of 3 (f=0.90) is less than those computed for a cyano (f = 0.96) or an aldehyde (f = 1.07) substitution. In summary, the more covalent the electronic structure or, more
-
( 5 5 ) Mulliken, R. S. J . Am. Chem. SOC.1952, 74, 811-824.
Kanis et al. empirically, the greater the interactions found in the molecular orbital diagram, the greater the electron density in the bridging region and the larger the oscillator strength. The foregoing discussion was included in this contribution because ferrocenylbased chromophores not only have the largest organometallic B values discovered to date but also possess anomalously large MLCT oscillator strengths compared with most other organometallic We now contrast our description for electronic origin of the second-order response in ferrocenyl chromophores to that recently proposed in the literature.8 On the basis of a qualitative bonding discussion, the authors of the previous contribution suggest that (1) the low-lying excitations (assigned as MLCT transitions) and the higher lying excitations (assigned as ligand-to-ligand charge-transfer excitations) make significant contributions to (2) poor coupling between the metal center and the cyclopentadienyl ligand lowers the effectiveness of the metal center as a donor, (3) the ferrocenyl donor behaves very much like a methoxyphenyl donor on the basis of experimental evidence, and (4) the metal plays a key role in determining hyperpolarizabilities in these chromophores. Point 3 is probably the most important in contrasting organic and organometallic NLO chromophores and is in full agreement with our quantitative computations. Perhaps the primary disagreement between our results and those presented in ref 8 is the nature and relative importance of the two optical transitions in the ferrocenyl chromophores. In the previous work, a ground-state one-electron extended-Hiickel computation was performed on 3, and the charge-transfer excitations were inferred from the electronic structure resultsS8In contrast, the present approach allows a full analysis of the electronic origins of 3i, by computing the contribution of each linear optical excitation to the second-order response and by linking the spectral features with transitions between filled and unfilled molecular orbitals. From our computations, we find that the higher lying transitions are MLCT and not LLCT as previously proposed. We assert that the lower lying transitions are in fact ligand-field-based excitations of unusually (but not unprecedentedly) large oscillator strengths, in agreement with the assignments of Toma and co-~orkers,’”*~~ and not MLCT transitions as hypothesized by Marder, Cheng, et aL8 Reference 8 also concludes that the two-level model does not apply to the ferrocenyl chromophores because both optical transitions make significant contributions to p,,. This assertion can be tested by examining the relationships between experimentally determined linear and NLO properties for specific chromophores. For example, we see from the experimental dataa that the lowenergy peak for chromophore 4 occurs at 533 nm compared to 500 nm for chromophore 8. However, the experimental B value of the former is significantly less (4, 40 X cms esu-I) than that of the latter (8,66 X cm5 esu-I). In other words, a significant blue-shift in the low-energy transition is accompanied by a significant increase in the quadratic hyperpolarizability, in disagreement with conventional chromophore design phenomenology based upon minimizing the denominator of eq 11. In contrast, the correlation of /3 to the higher lying absorptions (4, 357 nm; 8, 377 nm) fits nicely within the traditional two-level design guidelines. Additional empirical evidence that the lower lying ferrocenyl excitations do not significantly contribute to comes from comparison with organic chromophores. Conventional organic chromophores containing charge-transfer excitations near 500 nm possess extremely large nonlinear optical responses, on the order of 150-300 X cms esu-’ (for hw = 0.65 eV).32 However, the NLO responses of the ferrocenyl chromophores are not nearly as large under comparable measurement conditions as would be expected ifthese low-energy transitions indeed govern the magnitude of the second-order response. Our calculations show that only the higher energy ferrocenyl excitations (MLCT) are necessary to understand the NLO response and that an appropriate two-level model does apply to this class of chromophores; the higher energy MLCT excitations dictate 0, while the lower frequency ligand-field-based excitations contribute little. Since the ‘ligand-field” transitions are not pure d-d excitations (vide supra),
a,,
J . Am. Chem. SOC.,Vol. 114, No. 26, 1992 10351
Organotransition Metal Chromophores
Table IV. Comparison of Experimental and ZINDO-Derived Molecular Hyperpolarizabilities along the Dipole Moment Direction (&) and the ZINDO-Derived Total Intrinsic Hyperpolarizability (&,) a t 1.91 r m (hw = 0.65 eV) for Various Chromium Arene Derivatives"
I oc,Cr.,,,,co
'bCO
Y
B"sc=pt
Byecca'c
pzQh
pIcalc
PtOtCalC
pexpt 6
14
H -0.8 -1.30 1.30 0.0 8.6 4.4 OCH3 -0.9 -1.36 1.50 0.6 8.6 4.7 16 NH2 -0.6 -1.27 1.42 1.1 8.8 5.5 1.12 1.4 8.9 5.5 17 N(CH3h -0.4 -0.91 18 COOCH3 -0.7 -1.79 4.28 -4.5 8.1 4.0 19 trans-st yrenyl -2.2 -3.93 4.80 0.8 8.6 4.0 Also included is the calculated dipole moment in the x and z directions as defined above. All N L O data are in units of ems esu-l; all dipole moment data are in units of debyes. Negative dipole moments are indicative of negative charge buildup in the positive coordinate direction. bDipolar and nonlinear optical data from ref 7.
I5
a small additional contribution to j3, can be anticipated. Unfortunately, the broad LF transitions in the 400-550-nm range, while contributing little to the 0, will substantially diminish the useful optical transparency window of ferrocenyl chromophores in this energy region. The present ZINDO results, in agreement with those in ref 8, show that the metal-containing fragment plays a key role in determining the NLO response in these ferrocenyl chromophores. However, by virtue of the electronic similarities between the ferrocenyl donor and a conventional organic donor, the effect of incorporating the former fragment is both predictable and easily understandable in tems of conventional chromophore design wisdom. Also in accord with the previous work, our results argue for an operational equivalency between the methoxyphenyl donor and the ferrocenyl fragment. However, the methoxyphenyl donor is not an exceptionally potent T .electron donor by organic chromophore standards, and therefore, the magnitudes of the ferrocenyl NLO responses, while large relative to those of most transitionmetal-based chromophore^,^^^ are modest relative to those of efficient r-organic chromophores. Our M O analysis indicates that the iron center does efficiently couple to the organic ligand. It is precisely this property that gives the ferrocenyl complexes their organic-like NLO characteristics and leads to the large ferrocenyl j3 responses relative to those of many other classes of organometallic chromophores (vide infra). For example, the large oscillator strengths observed for these molecules can be directly related to the covalency of the ferrocenyl-ligand interaction, as shown in Figure 8. The ferrocenyl chromophores examined in this section have proven to be readily understandable in terms of traditional chromophore design guidelines. In contrast, most organometallic chromophores studied to date reveal that the ferrocenes are the exception rather than the rule. ZINDO-SOS computations on the chromium arene tricarbonyls identify features unique to organometallic chromophores. Chromium Arene Derivatives. The next class of molecular chromophores to be investigated are (t16-C6H6)Cr(C0)3-baSed architectures (14-31, Figure 11). These classic organometallic structures are representative of a broad range of transition-metal species containing low-valent metal centers. For this reason, the findings from detailed ZINDO-SOS analyses of chromium arene chromophores should apply to many low-valent organometallic structures. In our discussion, the parent chromium arene (14) will serve as the prototype for this class of chromophores. Before we discuss the ZINDO-SOS computed responses for the chromium complexes, it is useful to summarize the predominant electronic structure features as given in the literature. The Cr(CO), fragment is generally accepted as a strongly electronwithdrawing fragment in $-arene structure^.^^-^^ This charac(56) (a) Muetterties, E. L.; Bleeke, J. R.; Wucherer, E. J.; Albright, T. A. Chem. Rev. 1982.82, 499-525. (b) Silverthorn, W. E. Ado. Organomet. Chem. 1975, 13. 47-137. (57) Carroll, D. G.;McGlynn, S . P. Inorg. Chem. 1968, 7, 1285-1290.
15, Y = OCH, 14,Y.H 16, Y = NH, 17, Y = N(CH,), 18, Y = COOCH,
-
21, n = 1
19, n 1, Y = H 20, n = I,Y =NO, 22, n = 2. Y =NO, U , n = 3, Y = NO,
23, n = 2 2S,n=3
X
X Y
Y
oc ,CL ,TO
co
26, n = I . X -NH,. Y -NO, 27,n = 1. X = NO,, Y "H, 29,n= 2. X "H,.Y = NO, 3O.n =2. X =NO,, Y = h'H,
28, n = I.X = NH,. Y = NO, 31, n = 2, X = NH,, Y = NO,
Figure 11. Chromium arene chromophores examined in this study along with molecular identification scheme.
teristic is readily seen in metrical parametersSs as well as in chemical proper tie^.^^ Our ZINDO-SOS computations confirm that the Cr(C0)3 moiety is acting as an electron-withdrawing group in 14. Specifically, the calculated dipole moment of +8.6 D (Table IV) for 14, oriented in the z direction, reveals that the three carbonyl ligands act as electron acceptors in the ground state of ($-C6H(,)Cr(Co),. Previous spectroscopic and theoretical studies have analyzed the dominant excitations in c~(co)657'6"'61 and ( T ~ - C ~ H ( , ) C ~ ( C OThe ) ~ .lowest ~ ~ , ~lying ~ MLCT band in the former is assigned to a d,-to-CO 2 ~ excitation, * and the latter is usually assigned to a d,-to-arene A* with some admixed d,to-CO 2 ~ chara~ter.~' * If this MLCT transition dictates the NLO response in 14, we should expect that j3, will be negative, since the ground-state dipole moment is directed toward the carbonyl ligands while the MLCT band is directed toward the T-C& ligand. (58) Rees, B.; Mitschler, A. J . Am. Chem. SOC.1976, 98, 7918-7924. (59) See, for example: Elschenbroich, Ch.; Salzer, A. Organometallics: A Concise Introduction; VCH: Weinheim. Germany, 1989. (60) Johnson, J . B.; Klemperer, W. G. J. Am. Chem. SOC.1977, 99, 7 172-7 . _ _177 ._.
(61) Kotzian, M.; Rosch, N.; Schroder, H.; Zerner, M. C. J. Am. Chem. SOC.1989. 1 1 1 , 1681-7696.
(62) (a) Lundquist, R. T.; Cais, M. J. Org. Chem. 1962.27, 1167-1 172.
(b) Yamada, S.; Nakamura, H.; Tshuchida, R. Bull. Chem. SOC.Jpn. 1960, 33,481-492.
10352 J. Am. Chem. SOC.,Vol. 114, No. 26, 1992
Kanis et al.
Table V. Comparison of Experimental and ZINDO-Derived Optical Maxima (Amax) and Associated Oscillator Strengths U, for the Chromium Arene Derivatives"
y-
oc
I
,Cr.,,,,
\&O
LF transition
Y 14 15 16
17
X"1C
H
292 294 278 218 213
OCH3 NH2 N(CH3)2
MLCT transition
i
AI
Xcak
f
acc
~ e i p bt
0.13 0.12 0.11 0.11 0.12
1.6 1.1 0.7 1.2 2.0
225 227 230 231 24 1 331
0.60 0.64 0.52 0.11
1.9 1.6 0.8 2.1 2.4 6.1
310 310 313 318 318 410
0.15 18 COOCH, 19 rrans-stvrenvl 0.14 "All energy data are in units of nanometers; all dipole moment data are in units of debyes. bSpectroscopic data in toluene from ref 7. Scbeme 111. Analysis of fl for Molecule 14 Two-level contribution ( & & ? ) Three-level contribution C&& Total (ho= 0.65 e19
8.- in units of loJo c
Ligand Field Transition
Metal-To-Ligand Transition
-2.4 -1.3
d ami'
Assumption I : Three-level terns scale 08 two-level terns. Therefore, understanding two-level t e r m will provide qualitative understanding of p.
60%of the total two-level contribution comes from one two-level term involving a MLCT at 225 nm with an oscillator strength of 0.60.
20% of the total two-level contribution comes &om another two-level term involving a ligand-field transition at 292 nm with an oscillator strength of 0.13.
Assumption 2: The two4euel contribution is dominated by two ercited states. Therefore, understanding these a i r e d states will provide a qualitative understanding of p.
Experimental nonlinear optical response data are available for six a r e ~ ~ e - C r ( C O chromophores )~ (14-19).' As shown in Table IV, the ZINDO-derived susceptibilities are in excellent agreement with EFISH results, with theory and experiment finding that all six chromophores possess negative second-order susceptibilities in accordance with our predictions. Note, however, that the magnitudes of &, for the arene chromophores are an order of magnitude smaller than those of the aforementioned ferrocenyl derivatives and two orders of magnitude less than those of the most efficient organic chromophores. In the discussion below, we will analyze the origin of these low quadratic hyperpolarizabilities and suggest presently unrealized arene-based molecular architectures for which the ZINDO model predicts large NLO responses. A priori, one possible source for the relatively small 8, values in the arene-Cr(CO), chromophores is that the charge-transfer excitation is not directed along the ground-state dipole moment axis (i.e., & 75%) is collinear with the dipole direction for the six chromophores with the exception of chromophore 18, where less than 50% of the intrinsic nonlinearity will be sampled by EFISH. Clearly, the inherently small N L O responses for this class of molecules are of electronic origin. The quantum chemical information provided by the ZINDO-SOS algorithm permits an understanding of the electronic features limiting &, in these structures. As shown in Scheme 111, the two-level contributions in the arene prototype 14 are approximately twice the three-level contributions and of opposite sign, in accord with the aforementioned observations for most chromophores. Thus, we have again reduced the nonlinear optical computations to an understanding of the linear optical characteristics. We note that a ZINDO study of the linear optical properties of the closely related molecule Cr(C0)6 has recently appeared.6' The authors find the ZINDO-derived optical characteristics of Cr(C0)6 to be in excellent agreement with the gas-phase optical data. The experimental and theoretical spectral features for Cr(C0)6 both include a highly allowed excitation in the UV near 225 nm. Interestingly, the chromium arenes also possess intense MLCT bands in the near-UV yet are found to have
Figure 12. The difference in electronic populations between ground state and two crucial excited states for the prototypical chromium arene derivative (14) as determined by ZINDO calculations. A negative population reflects an increase in electron density in the charge-transfer process.
very small nonlinear optical responses. As indicated in Scheme 111, two transitions dictate the NLO response of 14 within the framework of the SOS formalism. The lower energy transition (A = 292 nm, f = 0.13) comprises 20% cm5 esu-I) of the total two-level contribution. As (-0.5 X depicted in Figure 12, this excitation involves a small charge transfer from the carbonyl ligands to the arene fragment. However, obscured from the charge analysis is that 0.40 Cr d, electrons are promoted into Cr d, orbitals. As anticipated, the oscillator strength associated with such a LaPorte-forbidden, ligand-field transition is small and the resulting contribution to the NLO response from this excitation is small on an absolute scale. The higher energy excitation (A = 225 nm, f = 0.60) is responsible for 60% (-1.5 X cm5 esu-I) of the two-level contribution to & ., The magnitude of this dominant MLCT contribution to &, is significantly less than that for the representative ferrocenyl chromophore (14, -1.5 X cm5 esu-l; 3, 54.5 X cms esu-I). Clearly, the relatively small second-order responses observed for 14-19 are due to the modest contributions from the MLCT excitations. As shown in Table V, the MLCT transition for chomophore 14 is calculated to be found at 225 nm. Note, however, that this highly allowed transition is observed experimentally at 310 nm, somewhat red-shifted from the ZINDO-derived energy. The computed absorption energy is also slightly red-shifted in chromophores 15-19. Our computations suggest that this excitation is extremely sensitive to the exact choice of Cr-CO and C-0 bond lengths, and thiscould be the origin of the disparity between theory and experiment. Nevertheless, the ZINDO results provide great insight into the origin of NLO activity in these chromophores (vide infra). If the three ZINDO-derived crucial optical parameters cf, A, A p ) for the dominant MLCT in the prototypical ferrocenyl (3) and arene (14) chromophores are analyzed, the computed oscillator strengths are comparable (3,0.90;14,0.60), the calculated A of the transition is red-shifted in 3 (354nm) relative to 14 (225nm), and most significantly, there is a major disparity in the change in dipole moments computed for the respective MLCT transitions (3,14.1 D, 14, 1.9D). Figure 12 shows the difference in regional charge between ground state and appropriate excited state for 14. Note that significant electron density (0.30electrons) is transferred to the *-ligands in this MLCT transition. However, the
J. Am. Chem. Soc.. Yo/. 114. No. 26, 1992
Organorransirion M e r d Chromophores 2
0
-2
.. BY
.6
-8
-IC
-li
Figure 13 Uolccular orbital diagram for thc reprcrcniali\c chromium arcnc chromophon (141. The Cr(CO), fragment laklr rcpracnt the Cr or CO orbiialr t h a t dominate a gwcn CnCO,< frapmcnl orbiial
chargc-transfer elcaron density is nearly cquall! divided between the carbonyl and arene ligands. As a consequence. only a mode5t A" is associated with this d.-ligand I* transition. and this ultimately limits thc quadratic h)perpolariiability in 14. The MLCT transition i n 14 cannot be represented bv a single exoration between an occupied and unoccupied molecular orbital Rather. several configuration exotations paninpate in the MLCT absorption. This transition can bc understood from the ZINDOdcrived MO diagram for (q"-C,H,)Cr(COJ, (Figure 13). I n this diagram. we have chosen to partition thc molecule into a Cr(CO1, fragment and a benzene moiety. The fronticr molecular orbitals of both fragmcnts have been discussed previously."' The fragment orbital labels for Cr(COJ, appearing in Figure 13 reflect thc dominant atomic character of a particular fraement orbital. Fur cxample. the Cr "d." orbitals pcssess some C O charactcr. The ligand orbital combinations are deliberately simplified in this MO diagram. Spccificall). the six CO I* orbitals and the three C6H. I* ligand orbitals are all dcpicted as one "LCMO'. Since many of the transitions from the d. orbitals into the ligand I* orbitals arc LaPone-alloued. a number of thesc configuration transitions make modest contribution to B., through the M I.CT transition and therefore greatl) complicate our simple picture. Perhaps the most important observation from this MO diagram is that thcre is significant mixing betuccn the arene I ' and the CO 21' orbitals. resulting in unfilled molecular orbitab containing substantial arcne and CO character. Notc that onl) two of the three Cr d. orbitals are forced to bc degenerate for symmctr) rcasons. The near degeneracy of the third mctal r.orbital u i t h the other two rcllccts the pronounccd pseudo-octahedral electronic symmetr! of this chromophorc. From the S L O (Table IV) and lincar optical (Table V ) data for chromophores 15-19. it is clear that the above conclusion^ for 14 are applicable to other chromium arene stmeturcs inespcctive of arcnc nng dcnvatization. Spxificall). the 4c values calculated for all the six arene chromophorcs arc far belou the 15-20 D computed for high-8 organic or ferrocen)l chromophores Thcrcforc. wen though some of the oscillator strengths calculated for the dominant 5II.CT in these molecules are rcnsonabl? large. the electronic pscudos)mmetr) dictates that their \LO responm will be small. iioie that even though the computed energ! of the CT excitation may be somewhat blue-shifted relative to experi(63) Albrighi. T. A,: Burdell. J. K.: W h a n p b . in Chrmirln: Wileg: N e w York. 1985.
M.H. Orbirol Inrrrorriom
10353
ment, the electronic asymmetry between the two ligands is related to the difference in orbital energies between the two sets of rligands and should therefore be obtained regardless of the disparity between observed and computed A. The general trend in the computed and experimental 8 values (Table IV) is rationalized as follows. Since the ground-state dipole moment is essentially unaffected by derivatization of the $benzene ring (Table IV), it is always directed toward the CO ligands. In addition. the MLCT direction is always slightly skewed toward the arene ring; thus, the antiparallel nature of the ground-state dipole moment and the charge-transfer direction dictates that 8 will be negative for chromophores 14-19. When an electron-withdrawing substituent (18, 19) is appended to the arene ring, the orbital energy of the arene-r* orbital is lowered, thereby red-shifting the MLCT transition and increasing &,,. Electrondonating substituents will clearly have the opposite effect. thereby decreasing the second-order NLO response. Recall that the calculated value of &,. the intrinsic N L O susceptibility. is positive by definition. Note that the smallest 8,,, is calculated for the molecule with the strongest donor (17, 1.12 X IO-''cm' esu-I). while the largest values of 8, are praliaed for the strongest acceptors (18,4.28 X iO-'O cm' esu-I; 19, 4.80 X IF" cm'esu-'). However, the calculated and experimental &,values for IS are nearly equal to those of 14-17 rather than 19. As illustrated by its ground-state dipole moment, the charge-transfer direction (2) is not parallel to the dipole moment direction (x and z ) in IS. Therefore, the EFlSH and ZINDO-derived 8,, values (-0.7 X I O - ' O cm' esu-' and -1.79 X cm' esu-I. respectively) are somewhat smaller in magnitude than the computed total susceptibility (4.28 X cm'esu-') (Table IV). Overall. however. chromophores 14-19 all display pseudo-octahedral electronic symmetry about the metal and therefore exhibit very small NLO responses irrespective of the substituents attached to the arene ring. The obvious prescription for enhancing 8,- via exploitation of the highly allowed charge-transfer transitions observed for the chromium tricarbonyl complexes would be to remove the aforementioned electronic pseudosymmetry. One potential solution would increase the *-conjugation length in the organic arene ligand, in analogy to the I-ferrocenylethylene chromophores. For this purpose, ZINDO-SOS N L O response calculations were carried out on hypothetical arene chromophores 20. 22. 24. 26, 27.29, and 30 and the organic analogues 21,23.25.u). and 31. Three points are readily apparent from the theoretical results reported in Table VI: ( I ) the p,, values for the hypothetical arene complexes are significantly less than those in the Cr(CO),-free analogues, (2) the computed 8.- values are markedly less than the p,,, values for all hypothetical Cr(CO),-derivatized chromophores examined. and (3) the &, values are posiriue for these arene molecules, in direct contrast to the negative quadratic hyperpolarizabilities found for chromophores 14-19. These unexpccted results will serve to illustrate some of the potential problem associated with organometallic chromophores in general. When electronically -inert" d electrons are involved in the MLCT transition that dictates 8 (within the SOS formalism). there is a question as to whether the total second-order nonlinearity (&,) will, in fact. be sampled by EFlSH (&,). That is. the principal charge-transfer direction may not coincide with the ground-state dipole moment direction. This is not a concern in most organic systems where orbitals that dictate the ground-state dipole moment are almost invariably involved in the primary I to 'r charge-transfer transition. However, in the arene complexes of interest here, the electron density of all occupied molecular orbitals (i.e.. dipole moment) indicates that there is a charge buildup on the carbonyl fragments in the 2 direction. As anticipated, altering the arene substituents in 14-31 has essentially no effect on the magnitude of p,. as reported in Tables IV and VI. What will change, however, is the magnitude of p, as the arene fragment is derivatized with better acceptors or modified to afford increased r-delocalization lengths. In molecule 20. for example. p: = 8.4 D and p x = -6.6 D. I n contrast. the ferrocenyl chromophores of the previous section have very small p, compo-
10354 J. Am. Chem. Soc., Vol. 114, No. 26, 1992
Kanis et al.
Table VI. ZINDO-Derived Molecular Hyperpolarizabilities along the Dipole Moment Direction (&) and ZINDO-Derived Total Intrinsic Hyperpolarizabilities (@tot) at 1.91 pm (hw = 0.65 eV) for Hypothetical Chromium Arene Derivatives" X
1 Cr 8.3 23.5 -6.6 8.4 20 H NO2 1 27.5 27.5 -7.5 0.0 21 H NO2 2 Cr 11.5 28.4 -6.1 8.5 22 H NO2 2 41.9 42.0 -7.8 0.0 23 H NO2 15.6 34.5 -6.8 8.6 24 H NO2 3 Cr 25 H NO2 3 57.6 57.9 -8.1 0.0 26 NH2 NO2 1 Cr 10.7 23.6 -7.8 8.7 NH2 1 Cr 14.8 26.6 8.8 7.3 21 NO2 1 46.4 46.5 -9.5 0.0 NO2 28 NH2 2 Cr 16.2 31.2 -8.0 8.8 NO2 29 NH2 2 Cr 27.5 41.4 9.2 7.3 NH2 30 NO2 2 65.7 65.9 -9.8 0.0 31 NH2 NO2 "Also included is the calculated dipole moment in the x and z directions as defined above. All NLO data are in units of cm5 esu-I; all dipole moment data are in units of debyes. A 'Cr" designation indicates that the chromophore contains a Cr(CO)3 moiety in the indicated position; no designation is indicative of a metal-free ligand.
Px
(Charge-TransferDirection)
Figure 14. Figure displaying the noncoincidence of ground-state dipole moment direction and principal charge-transfer direction in 20. The arrows are directed toward areas of increased electron density.
-
-
nents (Table I), and therefore px kOt and &e Blot. As shown schematically in Figure 14, the dipole direction in 20 bisects the x and z directions, while the primary charge-transfer direction is in the arene xy plane. For this reason,the ZINDOSOS results suggest that only 30% of the NLO response of 20 (btOt= 23.5 X cm5 esu-I) will be observable cm5 e s d , &, = 8.3 X in EFISH experiment^.^^ The positive second-order susceptibilities for the hypothetical arene chromophores listed in Table VI also provide insight into the electronic origin of the N L O response in these structures. From the previous discussion, any NLO component in the z direction should possess a negative In contrast, the dipole moment in the arene plane is directed toward the NOz moiety, as is the charge-transfer direction. In analogy to the case of the ferrocenyl chromophores or traditional donoracceptor *-organics, the fl component within the arene plane should therefore be positive. That the ZINDO-SOS-derived &, responses for these hypothetical chromophores are invariably positive provides strong evidence that x is the charge-transfer direction and not z as for chromophores 14-19. The ZINDO-SOS results (Table VI) show that the metal-free molecules (21,23,25,28,31) possess larger NLO responses than the corresponding metal-complexed structures. For example, the computed /3tot for the n = 3 metal-free arene (24,57.9 X cm5 esu-I) is significantly enhanced relative to the Cr(C0)3-cocm5 esu-I). In the ordinated chromophore (25, 34.5 X metal-free structures 21, 23, and 25, the unsubstituted phenyl group acts as a weak donor coupled through the *-backbone to the nitro acceptor to afford only modest second-order responses. (64) Note that the computed responses for the arene chromophores given in Table VI are very sensitive to metrical input parameters, particularly the C r C O distances. Nevertheless, for any reasonable choices of metrical parameters, the qualitative conclusion remains the same: an q6 coordination of a Cr(CO), fragment induces a ground-state dipole component perpendicular to the MLCT direction if introduced into an extended organic *-electron system.
Complexing the fragment reduces the intrinsic nonlinearity and lowers the calculated & due to the aforementioned dipole moment problem. As the conjugation length in the Cr(CO),-coordinated molecules is increased from n = 1 through n = 3, the computations indicate that only a modest increase in &,, is observed (23.5 X cmsesu-l for n = 1; 34.5 X cms esu-l for n = 3), while the analogous metal-free chromophores behave as conventional organic structures with an increasing &, (-Ptot) from 27.5 X 1C30cm5esu-l for 21 to 57.9 X 1C30cmsesu-' for 25. In addition, if we take reasonable donor-acceptor chromophores and functionalize one of the aromatic rings with a Cr(CO), group, the computed optical nonlinearity drops significantly regardless of which ring is functionalized, as shown in Table VI for molecules 26,27,29, and 30. Ironically, if the Cr(CO), group is coordinated to either an acceptor- or donor-function-based phenyl ring, the effect on /3 is virtually the same. The hypothetical arene chromophore with three ethyleneic units (24) fits within the two-level model and offers the possibility of a detailed delineation of the computed quadratic hyperpolarizability. Specifically, the ZINDO-derived two-level contribution = 42.4 X cm5 esu-I) is nearly twice the for 24 three-level contribution (bW3 = -26.9 X lC30 cm5em-'), in a m r d with results for most other nonlinear optiphoric structures. Approximately 70%of the total two-level contributions derives from one excitation, the MLCT described in Table VII. The metal-free analogue of 24 and 25 also fits the two-level descriptions, and one charge-transfer transition dominates the NLO response. Details of the dominant charge-transfer transitions in 24 and 25 are given by the change in electron density associated with the dominant excitation (Figure 15). The excited state is localized on the nitro group in both chromophores; however, the nitro substituent gains more electron density (Le., charge transfer is greater) in the metal-free chromophore than with the Cr(CO)3 group attached. Specifically the phenyl-N02 acceptor moiety gains 0.57 electrons in the isolated ligand via a LLCT and only 0.47 electrons using the MLCT in the arene derivative. The computed A p values given in Table VI1 for the metal-complexed (8.2 D) versus the metal-free (12.6 D) chromophore are in agreement with the results from Figure 15. The data in Table VI1 indicate that converting the LLCT in the organic arene into a MLCT by adding an Cr(C0)3 moiety will universally decrease A p by 30-70%. From Table VII, we see that the calculated ,A, of 24 and 25 are essentially identical (-395 nm); however the oscillator strength for the metal-free molecule (1 3 6 ) is somewhat greater than that for the metal-complexed molecule (1.45). Thus, complexing the Cr(CO)3 fragment to an organic ligand will decrease the magnitude of the charge transfer and decrease the
J . Am. Chem. SOC.,Vol. 114, No. 26, 1992 10355
Organotransition Metal Chromophores
Table VII. Comparison of Experimental and ZINDO-Derived Optical Maxima (Amax) and Associated Oscillator Strengths U, for Several Chromium Arene Derivatives"
oc
,Cr,,,,, MLCT transition
X 20 21 24
H H
Y
n
NO2 NO2 NO2 NO2 NO2 NH2
1 1 3 3 1 1 1
X"'C
Cr
368 355 393 398 316 34s 315
f
AP
0.24 1.13 1.45 1.86 0.14 1.45 1.19
9.2 12.8 8.2 12.6 6.5 6.8 14.8
H Cr H Cr 26 NH2 21 NO2 Cr NH2 28 NO2 All energy data are in units of nanometers. A "Crn designation indicates that the chromophore contains a Cr(CO)3 moiety in the indicated position; no designation is indicative of the a metal-free ligand with no Cr(CO)3 group attached.
25
--0.10
+0.03
5
-0.37
4.06
'.
67
/I\ co co
2
I 4.22 co
14.11
4.08
--0.12
--0.19
4.20
-0.02
-0.45
-0.42
14.43
Figure 15. The difference in electronic populations between ground state and &dominating excited state for Cr(CO)3-arenederivative (24), the metal-free arene (25), and a Cr(NH&-arene derivative (32), as calculated by ZINDO. A negative population reflects an increase in electron density in the charge-transfer process.
oscillator strength of the @-dominatingtransition. The mechanism of charge transfer for ( q 6 C6H~-(C2H2)3-C6H4-N02)Cr(CO)3 can be probed further by examining the ZINDO-derived molecular orbital diagram for the prototypical chromophore (Figure 16). The dominant chargetransfer excitation in this chromophore, as computed through configuration interaction, is found to be 60% HOMO LUMO and 25% HOMO SLUMO. Since the energy and orbital makeup of the LUMO and SLUMO are virtually identical, we will focus on the orbital origin of the HOMO LUMO excitation. As for the ferrocenyl derivatives, there is a strong covalent interaction between the d.+? orbital and the arene mystem which serves to break the degeneracy of the three d, orbitals (i.e., destroy the octahedral pseudosymmetry about the metal). The calculations also suggest that the LUMO and SLUMO are predominantly localized on the arene ligand, in contrast to the (?6-C6&)Cr(Co)3 (14) LUMO, which contains nearly equal amounts of arene and CO character. As a consequence, the charge-transfer excitation is much more unidirectional in 24 than in 14, as evidenced by the larger values of Ap. In the isolated ligand, the HOMO LUMO (r r*) transition dictates the second-order NLO response. From Figure 16, we see that the energy of the HOMO LUMO
-
-
-
-
-
-
-
transition in the metal complex is nearly identical to that of the r r* transition calculated for the metal-free ligand, in agreement with the similarities in the optical absorption energies for the two chromophores (Table VII). In summary, we can state that the electronic origin of the second-order response in this class of arene chromophores is very similar to that found for the ferrocenyl derivatives. A covalent interaction between the organic ligand and the metal fragment creates an asymmetric environment about the chromium atom, leading to modest second-order responses. From the computed /3 data in Table VI, it is clear that the inherent responses (&,J in Cr(C0)3-substituted organic structures are lower than those in their metal-free organic analogues due to the low A p values associated with the dominant charge-transfer excitation. Essentially, the CO ligands are weak acceptors which reduce the donating strength of the d, orbitals in the chromium arene chromophores. Therefore, even very asymmetric metal-arene structures are not nearly as asymmetric as conventional organic structures. In addition, the noncoincidence of the ground-state dipole moment and the charge-transfer directions dictates that significant portions of the modest secondorder responses in this class of chromophores will not be sampled with EFISH nor would conventional poling techniques achieve optimum x ( ~ values ) for polymer matrices containing these chromophores. It is apparent that the above features are serious drawbacks to using this class of organometallic chromophores in NLO materials. Moreover, it is clear that these shortcomings will not be limited to this particular class of organometallic structures. As stated previously, it is not uncommon for an MLCT transition originating from a relatively nonbonding d, orbital to be nonparallel to the ground-state dipole moment direction. In regard to the more serious second shortcoming of the arene complexes, the small Ap values associated with the MLCT excitations, these should also be representative of most organometallic chromophores where the metal is strongly coupled to the organic ligand. This can be seen by noting that the ligands surrounding a metal center usually reflect the electronic characteristics of the metal center. Hard ligands (NH3, H 2 0 , oxides, sulfides) are preferentially coordinated to highly oxidized metal centers, while soft ligands (CO, CN, C6H6) prefer reduced centers. In a low-valent environment, for example, the degree of *-basicity can be varied to create a somewhat asymmetric environment; however, substituting one soft base for another will only lead to small A p values and modest NLO responses. To truly destroy the electronic pseudosymmetry about a metal center, hard ligands must be coordinated trans to soft ligands about the metal center. To test this hypothesis, we computed the NLO response for a molecule conforming to the above specifications (32). Specifically,
10356 J. Am. Chcm. Sac.. Vol. 114. No. 26, 1992 2
Kanis et a/.
-
...........___. -b
co Zlt'
,
0
-2
-4 eV
-6
-8
-10
Flyre 16.
-1 2 Molecular orbital diagram for 24. The Cr(CO), fragment lakls represent the Cr or CO orbitals that dominate a given Cr(CO), fragment
orbital.
ev-41
.,....
-6
-8
Figure 17. Molecular orbital diagram for chromophore 32. The Cr(NH,), fragment lakls represent the Cr atomic orbitals that dominate a given Cr(NH,),
fragment orbital.
a reduced Cr center is surrounded with both hard, electron-releasing NH, ligands and a soft arene ligand. Essentially. three
ammine ligands are substituted for the three "LO-inactive" *-accepting CO ligands in chromophore 20. While 32 is strictly
OrganotransitionMetal Chromophores
a hypothetical molecule, it illustrates the potential of including hard and soft ligands around a metal center. The ZINDWerived &, for 32 is 780 X cmsesu-l at ho = 0.65 eV, a very large second-order response. In fact, the computed quadratic hyperpolarizability for 32 rivals the largest quadratic hyperpolarizabilities reported for any conventional organic chromophore. A sizeable portion of &, for 32 is resonance-enhanced due to a 757-nm charge-transfer transition; however, note that the static cms esu-' rivals or value of &, (ha = 0.0 eV) of 245 X exceeds any Bstaticcomputed to date for a conventional organic chromophore. By comparing the computed response (&, (ho = 0.65 eV)) of 32 (780 X cmsesu-') to that of the metal-free ligand (21,27.5 X cms esu-I) and the analogous Cr(C0)3 structure (20,8.3 X cm5 esu-I), we see that the Cr(NH3)3 derivatization significantly enhances the NLO properties of an arene fragment, while a coordinated Cr(CO)3 moiety acts as a detriment. The Cr(NH3)3-appended chromophore fits our empirical two-level model, and therefore an analysis of the dominant charge-transfer transition will provide a detailed understanding of the electronic origin of the NLO response in this novel molecule. The transition dictating the second-order response of 32 is calculated to be at 757 nm with an oscillator strength of 0.45 and a Ap of 15.6 D. In contrast to the case of the Cr(CO),-coordinated arenes, the important optical transition in 32 possesses a large charge-transfer component. The population redistribution associated with the charge-transfer transition (Figure 15) rationalizes the computed value for Ap, These electron density differences show that more metal electrons are involved in the chargetransfer excitation in 32 than in a related Cr(CO),-functionalized arene molecule, suggesting that Cr(NH3)3is acting as a stronger donor than Cr(CO)3. The energetics of the computed optical excitation can be explained from the MO diagram of 32 (Figure 17), since most of the dominant chargetransfer transition (>85%) is HOMO LUMO. The interaction picture shows that the orbital energies of the metal d, orbitals are raised significantly relative to the energies found in Cr(C0)3 arenes due the presence of electronreleasing N H 3 ligands. In fact, they are now at energies comparable with those of the ligand A* orbitals rather than the u orbitals as was true for all ferrocenyl and Cr(CO), derivatives. The presence of such a high-lying filled set of metal orbitals maka the Cr(NH3)3fragment a superb donor. The d+p metal orbital is the key metal function involved in the bonding interaction. It interacts with both the filled and unfilled frontier orbitals of the
-
J. Am. Chem. Soc., Vol. 114, No. 26, 1992 10357 metal-free fragment to form the HOMO and LUMO of the complex. As anticipated, the three d, orbitals are removed from one another energetically, reflecting the large electronic asymmetry in 32. In addition, we see that the ground-state dipole moment in the z direction is now directed toward the arene (p, = -12.70 in 32,pz = 8.4 D in the Cr(CO), analogue 20) by virtue of the strongly donating ammine ligands. Thus a much larger percentage of the intrinsic 6 would be sampled by EFISH in the Cr(NH3)3-substitutedchromophore (-80% in 32) than in one of the Cr(CO)3 derivatives. Conclusions Our calculations suggest that if organometallic chromophores are to compete with conventional u-electron donor-acceptor molecules as building blocks for macroscopic second-order NLO materials, the strongly coupled ligation sphere around a given metal must be highly polarized. Only in a very asymmetric environment will the schematic representation (Figure 1) of enhanced NLO responses via organometallic architectures be realized. Unfortunately, most stable organometallic molecules tend to possess electronic pseudosymmetry, and therefore the MLCT transitions one would wish to exploit for NLO responses will not possess significant, unidirectional charge-transfer character. Perhaps the most important conclusion from this contribution is that efficient quantum chemical methods can be used to understand molecular quadratic hyperpolarizabilities in terms familiar to practicing chemists. These conclusions can then be employed to design new chromophoric units possessing optimal NLO characteristics, and such efforts are continuing in our laboratories. Future publications will address exploiting LMCT excitations, exploiting MLCT transitions in VI-coordinated structures, using novel conjugation architectures in potential NLO chromophores, as well as discussing the role of three-level contributions in the NLO response.
Acknowledgment. This research was supported by the NSFMRL Program through the Materials Research Center of Northwestern University (Grant DMR882157 1) and by the Air Force Office of Scientific Research (Contract 90-0071). We thank Professor Michael Zemer for graciously supplying us the ZINDO program and the Pittsburgh Computing Center and Cray Research Inc. for providing supercomputing resources. We also thank Drs. G. R. Meredith, L.-T. Cheng, W. Tam, and S. R. Marder for information in advance of publication.
